\section{Introduction}
The existence of dark matter (DM) in our Universe has been well established by astrophysical and cosmological observations. To explain this, one needs some new particle(s) and symmetries beyond the Standard Model (SM). Being colorless and electrically neutral, SM-singlet right-handed neutrino (RHN), introduced in seesaw models to explain the small neutrino mass, is a natural DM candidate. However in the conventional seesaw models\cite{type1a, type1b, type1c, type1d, type1e}, its Yukawa couplings to SM lepton and Higgs doublets make it highly unstable, and therefore, unsuitable for DM, unless its mass is in the keV range with appropriately small Yukawa couplings\cite{Adhikari:2016bei}. In ultraviolet (UV) complete scenarios of seesaw, e.g. those based on the Left-Right (LR) gauge group $SU(2)_L \times SU(2)_R \times U(1)_{B-L}$~\cite{LR1, LR2, LR3}, the gauge interactions of RHNs induce further decay modes, which have to be suppressed/forbidden by imposing additional discrete symmetries (or making the model more contrived) to keep the lightest RHN cosmologically stable\cite{Fiorentin:2016avj}.

In this paper we discuss an alternative class of LR models based on the gauge group $SU(3)_c \times SU(2)_L\times SU(2)_R\times U(1)_{Y_L}\times U(1)_{Y_R}$~\cite{Dev:2016xcp} which has an accidental $Z_2$ symmetry, at the renormalizable level that keeps the lightest RHN stable making it a natural DM candidate. In this model there exists a right-handed copy of the SM electroweak sector at the TeV scale (or higher), charged under $SU(2)_R \times U(1)_{Y_R}$. The breaking of this gauge symmetry down to $U(1)_{\rm em}$ is similar to the LR models with universal seesaw\cite{Babu:1989rb,CP1,CP2}. But one of the key differences from the universal seesaw models is that the right-handed lepton sector in our model is prevented by gauge symmetry from having any masses connecting the heavy sector to the light ones. Because of this, there appears a remnant automatic $Z_2$ symmetry in the leptonic sector at the renormalizable level that keeps the lightest RHN stable.
If the stabilizing $Z_2$ symmetry is softly broken by a mass term connecting the heavy and light sector, the RHN DM can be made very long-lived but allowing for its decay into SM leptons.
This raises the possibility that for a PeV-scale DM, one can explain the ultra-high energy neutrino events observed at IceCube~\cite{Dev:2016qbd}. We also point out a dilution mechanism which allows us to relax the unitarity bound on the dark matter to the PeV mass level so that it can be applied to the discussion of PeV neutrinos in the context of a thermal annihilating DM.

\section{The Model}
\label{sec:model}

The model is based on the gauge group $SU(2)_L \times SU(2)_R \times U(1)_{Y_L} \times U(1)_{Y_R}$.~\cite{BCS,BCS2} For each generation of SM fermions
\begin{eqnarray}
&& Q_{L} \ \equiv \ \left(\begin{array}{c} u\\ d\end{array}\right)_{L}: \bigg({\bf 2}, {\bf 1}, \frac{1}{3}, 0\bigg), \quad
\psi_{L} \ \equiv \ \left(\begin{array}{c} \nu \\ e \end{array}\right)_{L}: ({\bf 2}, {\bf 1}, -1,0) , \nonumber \\
&& u_R: \bigg({\bf 1}, {\bf 1}, \frac{4}{3}, 0\bigg),~~
d_R: \bigg({\bf 1}, {\bf 1}, -\frac{2}{3}, 0\bigg),~~
e_R: ({\bf 1}, {\bf 1}, -2, 0) ,
\end{eqnarray}
we have the heavy fermion partners
\begin{eqnarray}
&& \mathcal{Q}_{R} \ \equiv \ \left(\begin{array}{c} \mathcal{U} \\ \mathcal{D} \end{array}\right)_{R}: \bigg({\bf 1}, {\bf 2}, 0, \frac{1}{3}\bigg), \quad
\Psi_{R} \ \equiv \ \left(\begin{array}{c} N \\ \mathcal{E} \end{array}\right)_{R}: ({\bf 1}, {\bf 2}, 0, -1), \nonumber \\
&& \mathcal{U}_L:\bigg({\bf 1}, {\bf 1}, 0, \frac{4}{3}\bigg),~~ \mathcal{D}_L:\bigg({\bf 1}, {\bf 1}, 0, -\frac{2}{3}\bigg),~~
\mathcal{E}_L:({\bf 1}, {\bf 1}, 0,-2) \, .
\end{eqnarray}
The Higgs sector of the model consists of $SU(2)_{L,R}$ doublets and triplets:
\begin{align}
& \chi_L \ = \ \left( \begin{matrix} \chi_L^{+} \\ \chi_L^0 \end{matrix} \right)  : ({\bf 2}, {\bf 1}, 1, 0) \,, \qquad
\chi_R \ = \ \left( \begin{matrix} \chi_R^{ \, +} \\ \chi_R^{\, 0} \end{matrix} \right)  : ({\bf 1}, {\bf 2}, 0, 1) \,, \nonumber \\
& \Delta_L \ = \ \left(\begin{matrix}\frac{\Delta^+_L}{\sqrt{2}} & \Delta^{++}_L\\ \Delta^0_L & -\frac{\Delta^+_L}{\sqrt{2}}\end{matrix}\right)  : ({\bf 3}, {\bf 1}, 2, 0) \,,  \qquad
\Delta_R \ = \ \left(\begin{matrix}\frac{\Delta^+_R}{\sqrt{2}} & \Delta^{++}_R\\ \Delta^0_R & -\frac{\Delta^+_R}{\sqrt{2}}\end{matrix}\right)  : ({\bf 1}, {\bf 3}, 0, 2) \,.
\end{align}
The SM $SU(2)_L$ and new $SU(2)_R$ gauge symmetries are broken by the vacuum expectation values (VEV) of the neutral components of these Higgs fields:
\begin{align}
\langle \chi_L^0 \rangle  =  v_{L} \equiv v_{\rm EW}, \qquad \langle \chi_R^{0} \rangle  =  v_R, \qquad \langle \Delta_L^0 \rangle  =  w_L,\qquad  \langle \Delta_R^0 \rangle  =  w_R.
\end{align}
 The SM and heavy charged fermion masses are obtained through their Yukawa couplings to the Higgs doublets:
\begin{eqnarray}
\label{eq:Lyukawa}
- \mathcal{L}_Y & \ \supset \ &
 y_{u}  \overline{Q}_L \widetilde{\chi}_{L} u_R
+ y_{d}\overline{Q}_L  \chi_{L} d_R
+ y_{e} \overline{\psi}_L  \chi_{L} e_R \nonumber \\
&& +y'_{u}  \overline{\cal Q}_R \widetilde{\chi}_{R} {\cal U}_L
+ y'_{d}\overline{\cal Q}_R  \chi_{R} {\cal D}_L
+ y'_{e} \overline{\Psi}_R  \chi_{R} {\cal E}_L
+ {\rm H.c.} \,,
\end{eqnarray}
where $\tilde{\chi}_L = i\sigma_2\chi_L^*$  and similarly for $\chi_R$ ($\sigma_2$ being the second Pauli matrix).
Exact parity symmetry implies that the Yukawa couplings $y_f = y'_f$ (and also $f = f'$ in Eq.~(\ref{eq:Lyukawa2}) below). If the $SU(2)_R$ symmetry breaking is at the TeV scale, there would be new quarks in the few GeV range, which is inconsistent with the current LHC bounds on vector-like fermion masses of order of TeV. To have heavy quarks and leptons at the TeV scale, we adopt the parity violating scenario in which the couplings $y_f$ and $y'_f$ are independent and choose $y'_f \sim {\cal O} (1)$.\footnote{The parity symmetric version could be realized at the TeV scale by doubling the doublet scalars in both the SM and heavy sectors, such that one set of the Yukawa couplings $y_{f,1}$ is responsible for the SM fermion masses and the other one $y_{f,2}$ dominates the heavy fermion masses~\cite{Dev:2016xcp}.} It is worth noting that at this stage the lower bound on $M_{W_R}$ from low-energy flavor changing effects such as $K^0-\overline{K^0}$ mixing does not apply to our model.

The masses of light and heavy neutrinos are generated from couplings to the triplet scalars $\Delta_{L,R}$ via the type-II seesaw mechanism~\cite{type2a, type2b, type2c, type2d}:
\begin{eqnarray}
\label{eq:Lyukawa2}
- \mathcal{L}_Y & \ \supset \ &
f \overline{ \psi_L^C} i\sigma_2 \Delta_L \psi_L
+ f' \overline{ \Psi_R^C} i\sigma_2 \Delta_R \Psi_R
+ {\rm H.c.} \,,
\end{eqnarray}
which implies that the VEV $w_L$ should be at the eV scale and $w_R$ is at the TeV scale or above. This can be easily obtained by choosing appropriate values of the parameters in the scalar potential.

\section{Depleting the heavy quarks}

After symmetry breaking at the right-handed scale and the electroweak scale, the model has a large global symmetry: $U(1)_{B,\,L}\times U(1)_{B,\,R}\times Z_{2\ell,\,L} \times Z_{2 \ell,\, R}$, with the two $U(1)_B$ the baryon numbers in the SM and heavy sectors, and the two $Z_2$'s the corresponding lepton numbers. Protected by the baryon number symmetry, the lightest hadron in the $SU(2)_R$ sector is absolutely stable, which can be one of the heavy baryons of form $QQQ$, $QQq$, $Qqq$, or heavy mesons $\bar{Q}Q$ and $\bar{Q}q$.

For the phenomenological purpose of avoiding the heavy lightest baryon also becoming DM and affecting the evolution of the Universe, we add two more Higgs singlets $\Sigma_1({\bf 1},{\bf 1}, -\frac43, +\frac43)$ and $\Sigma_2({\bf 1},{\bf 1}, +\frac23,- \frac23)$ which connect the heavy and light singlet quarks via the terms
\begin{eqnarray}
\label{eqn:Lmix}
{\cal L}_{\rm mix} \ = \ \lambda_U \overline{\mathcal{U}}_Lu_R\Sigma^*_1+\lambda_D\overline{\mathcal{D}}_Ld_R\Sigma^*_2+ {\rm H.c.} \,.
\end{eqnarray}
Once the $\Sigma$ fields acquire VEVs, the heavy-light quark mass mixing terms $\delta_{U} = \lambda_{U} \langle \Sigma_1 \rangle$ and $\delta_D = \lambda_D \langle \Sigma_2 \rangle$ appear in the Lagrangian, and the heavy quark can then decay into the SM fermions, leaving only the lightest RHN stable due to the leptonic $Z_2$ symmetry. The singlets $\Sigma_{1,2}$ are charged under $U(1)_{Y_L} \times U(1)_{Y_R}$ and break this symmetry down to $U(1)_{\cal Y}$. At this stage this model is similar to the usual LR models with $U(1)_{B-L}$, however with the quantum number $\cal Y$ different from $B-L$ and also from the SM hypercharge $Y_L$ (which is a linear combination of $\cal Y$ and the
$U(1)$ subgroup of $SU(2)_R$ after symmetry breaking).

The decay rate of heavy quarks $Q \to q + Z$ can be estimated as
\begin{eqnarray}
\Gamma_{Q} \ \simeq \ \frac{g_L^2}{64\pi \cos^2\theta_w} \frac{\delta^2_Q}{v_R^2} \frac{M_Q^3}{M_Z^2}\,,
\label{MQq}
\end{eqnarray}
where $\theta_w$ is the SM weak mixing angle and $g_L$ is the gauge coupling of $SU(2)_L$.
Requiring that the heavy quarks are depleted before the QCD phase transition epoch $T_{\rm QCD}\approx 200$ MeV imposes a lower bound on the magnitude of $\delta_{Q} \gtrsim 10^{-6}$ GeV~\cite{Dev:2016xcp}. When this limit is close to being saturated, we expect the heavy quark decay length to be several cm, leading to displaced vertex signatures at hadron colliders.

\section{Connecting the SM to DM}
\label{sec:2.4}

In absence of any scalar and fermion mixings connecting the heavy and light sectors, the RHN $N$ interacts \textcolor{red}{pairwise} with the SM fermions only through the heavy $Z_R$ boson, which couples directly to the SM sector through the $U(1)_{\mathcal Y}$ interaction. Once the mixing terms are included, at the lowest order, two $N$'s could also annihilate to the SM fields via the SM Higgs $h$ and $\Delta_R^0$ as well as the $Z$ boson, induced due to the $h - \Delta_R^0$ and $Z - Z_R$ mixings at tree level. The SM Higgs $h$ is assumed to be predominantly from the doublet $\chi_{L}$, and thus, the scalar mixing is expected to be of order $\zeta_S \simeq \lambda v_{\rm EW} / w_R$ from the quartic term $\lambda ( \chi_L^\dagger \chi_L ) {\rm Tr} ( \Delta_R^{\dagger} \Delta_R )$, where for simplicity we have neglected the mixing with other scalars. The neutral gauge boson mixing is of order $\zeta_Z\simeq \xi_Z(M_Z/M_{Z_R})^2$, where $\zeta_Z=\sin\theta_w(\cot^2\theta_w g_R^2/g_L^2-1)^{-1/2}$.
Note that when the gauge coupling $g_R$ approaches the theoretical lower limit~\cite{rizzo} $g_L \tan\theta_w$ (which is independent of the symmetry breaking pattern~\cite{Dev:2016dja}), the $Z - Z_R$ mixing could be significantly enhanced.

In the minimal version of our model, we do not have the bi-multiplet scalars which transform non-trivially under both $SU(2)_L$ and $SU(2)_R$, thus the charged gauge bosons $W$ and $W_R$ can not mix at the tree level. A tiny mixing arises at one-loop level, induce by the heavy-light quark mixings, which is estimated to be $\zeta_{W} \sim 10^{-12}$ for the third generation quarks, and even smaller for the first and second generations.

\section{DM annihilation and relic density}
\label{sec:3.2}

In the early universe, all the particles are in equilibrium due to the common $SU(3)_c$ color and $U(1)_{\mathcal Y}$ interactions.  As the universe cools down below the DM mass $M_N$, the DM density goes down and freezes out, as in case of a generic thermal DM candidate. The primary annihilation channels to the SM particles proceed via the scalar and the neutral gauge boson portals:
\begin{eqnarray}
NN \ \to \ \left\{\begin{array}{c} h^{(\ast)} / \Delta_R^{0 \, (\ast)} \\ Z^{(\ast)} / Z_R^{(\ast)}  \end{array} \right . \ \to \  \text{SM particles} \,.
\label{eq:ann}
\end{eqnarray}
The $h$ and $Z$ portals are suppressed respectively by the small mixing angles $\zeta_S$ and $\zeta_Z$. On the other hand, though the couplings of $Z_R$ to $N$ and the SM fermions are of order one, the $Z_R$ portal is suppressed by the large $Z_R$ mass, except for the Breit-Wigner resonance when $2M_N\simeq M_{Z_R}$. The $\Delta_R$ portal is suppressed when DM is light, as the Yukawa coupling $f'$ is proportional to the DM mass via $M_N = 2 f' w_R$. Combining all the available channels, we calculate the thermally averaged DM annihilation cross section times velocity $\langle \sigma v \rangle = a + b \langle v^2 \rangle + \mathcal{O} (v^4)$, from which the current DM relic density can be obtained via
\begin{eqnarray}
\Omega_N h^2 \ = \ \frac{1.07 \times 10^9 \, {\rm GeV}^{-1}}{M_{\rm Pl}} \frac{x_F}{\sqrt{g_\ast}} \frac{1}{a+3b/x_F} \,,
\label{eq:relic1}
\end{eqnarray}
where $x_F = M_N / T_F \simeq 20$ (with $T_F$ being the freeze-out temperature) and $g_\ast = 106.75$ is the relativistic degrees of freedom at $T_F$.

\begin{figure}[t!]
  \centering
  \includegraphics[width=0.6\textwidth]{density} \\
  \caption{An illustration of the relic density of RHN DM as a function of its mass $M_N$ for different values of $g_R/g_L$. The horizontal line gives the observed value from Planck data~\cite{Ade:2015xua}. }
  \label{fig:density}
\end{figure}

An example is given in Fig.~\ref{fig:density}, where we set explicitly the quartic coupling $\lambda = 1$ and the heavy scalar mass $M_{\Delta_R^0} = 2$ TeV with width 30 GeV. Three different value of the gauge coupling $g_R$ are chosen with $g_R / g_L = 0.6$, 1 and 1.5. The corresponding $Z_R$ mass and the RH scale $v_R = w_R$ are set to their current experimental lower bounds~\cite{Aaboud:2016cth}, viz. $M_{Z_R}=4.4, \, 3.3, \, 2.8$ TeV and $w_R=2.9, \, 2.6, \, 1.7$ TeV for $g_R/g_L=0.6, \, 1, \, 1.5$  respectively.
The horizontal dashed line shows the observed relic density, as measured by Planck~\cite{Ade:2015xua}. The various peaks in Fig.~\ref{fig:density} are respectively (from left to right) due to the SM $Z$ and Higgs bosons, $\Delta_R^0$ and $Z_R$.
We find that a TeV scale RHN could accommodate the observed DM relic density, with the annihilation dominated by the heavy scalar and/or $Z_R$ bosons, depending largely on the quartic coupling $\lambda$, the gauge coupling $g_R$ and the VEV $v_R$.

\section{Going beyond the unitarity bound}

In generic annihilating thermal DM models, the DM mass cannot be arbitrarily large due to the well-known partial wave unitarity limit~\cite{kamion}. To see this explicitly in our model, we write down the thermal averaged annihilation cross section at leading order in $v_{\rm EW}^2 / v_R^2$:
\begin{align}
\label{eqn:sigmav_pev}
\langle \sigma v \rangle
\ = \ & \frac{3 f^{\prime 2} \lambda^2  \langle v^2 \rangle}{64 \pi v_R^2} \frac{M_N^4}{(4M_N^2-M_\Delta^2)^2+M_\Delta^2\Gamma_\Delta^2}
+ \frac{\tilde{g}^4 M_N^2}{64 \pi M_{Z_R}^4}
\left( 1 - \frac14 \langle v^2 \rangle \right) \nonumber \\
& + \frac{(5 g_R^4 \tan^4\phi+\tilde{g}^4) \langle v^2 \rangle}{24\pi}
\frac{M_N^2}{(4M_N^2-M_{Z_R}^2)^2+M_{Z_R}^2\Gamma_{Z_R}^2} \,,
\end{align}
where $\tilde g^4 \equiv g_L^2 g_R^2 \xi_Z^2 / (16 \cos^2 \theta_w \cos^2 \phi)$.
Thus the cross section is suppressed by the right-handed scale $v_R$, i.e. $\langle \sigma v \rangle \propto v_R^{-2}$, except when $2M_N\simeq M_{\Delta}$ or $M_{Z_R}$, which results in a Breit-Wigner enhancement. Even in this case, we must ensure that the maximum value of the cross section at the resonance obeys the partial wave unitarity limit~\cite{Nussinov:2014qva}. For the resonance $R(=\Delta, Z_R)$ just above the threshold, Eq.~\eqref{eqn:sigmav_pev}  can be approximated by
\begin{eqnarray}
\langle \sigma v \rangle \ \simeq \ 16 \pi \, \frac{\Gamma_{NN}\Gamma_{\rm SM}}{(4M^2_N-M^2_R)^2+\Gamma^2_{R}M^2_R}
\ \sim \  \frac{4\pi} {M_N^2} \left( B_{NN}B_{\rm SM} \right) \,,
\label{eq:uni2}
\end{eqnarray}
where $\Gamma_{NN}$ and $\Gamma_{\rm SM}$ are the partial decay widths of $R$ to the DM pair and SM particles respectively, and $B_{NN}$ and $B_{\rm SM}$ are the corresponding branching ratios. From Eq.~\eqref{eq:uni2}, we find that the annihilation rate decreases with increasing DM mass, which leads to the unitarity bound. This is shown in Fig.~\ref{fig:uni} where we have fixed the $\Delta$ and $Z_R$ masses at the resonance and have varied the coupling $\lambda$ between $10^{-5}$ and $\sqrt{4\pi}$ to obtain the scattered points for the relic density as a function of the DM mass. We find that only the $M_N$ values between 1--20 TeV can explain the observed relic density in this scenario.

\begin{figure}[t!]
  \centering
  \includegraphics[width=0.6\textwidth]{unitarity.pdf} \\
  \caption{The relic density of RHN DM as a function of its mass $M_N$ at the resonance for different values of $\lambda$. The horizontal line gives the observed value from Planck data~\cite{Ade:2015xua}. }
  \label{fig:uni}
\end{figure}

It turns out that there is a built-in mechanism for entropy dilution in our model, thus making it possible to go beyond the unitarity limit.  The basic idea is that the next-to-lightest heavy neutrino (denoted here by $N_2$) does not need to be stable and can decay into SM leptons, e.g. $N_2 \to \ell \ell \nu$ via the charged lepton mixing terms in Eq.~(\ref{eqn:Lmix2}) involving only the heavier than $N$ leptons in the $SU(2)_R$ sector. Note that the hadronic channels $N_2 \to \ell q \bar q$ are comparatively further suppressed by the small quark mixing $\delta_Q$, and the two-body decay $N_2 \to W^\pm \ell^\mp$ is heavily suppressed by the loop-induced $W - W_R$ mixing.
Because of higher mass, $N_2$ freezes out before the DM $N$ but could decay after $N$ freezes out, i.e. $T_{N_2}< T_F$, with appropriate values of leptonic mixing.
The decay of $N_2$ to relativistic SM species will generate entropy which dilutes the relic density of $N$, and therefore, the initial relic density of $N$ can be significantly larger than the current value, thus allowing for larger $M_N$ values in Fig.~\eqref{fig:uni}.

The $N_2$ decay temperature is given by
\begin{eqnarray}
T_{N_2} \ \simeq \ 0. 78 g_\ast^{-1/4}\sqrt{\Gamma_{N_2}M_{\rm Pl}} \,,
\end{eqnarray}
where $M_{\rm Pl}$ is the Planck scale and the decay width
\begin{eqnarray}
\Gamma ( N_{2} \to \ell \ell \nu ) \ \simeq \
\frac{y_e^2 y_e^{\prime 2} N_{\rm lepton}}{96 \pi^3} \frac{M_{N_2}^5}{M_\Delta^4}
\left( \frac{\delta_\ell}{v_R} \right)^2 \delta_{S}^2 \,,
\end{eqnarray}
with $N_{\rm lepton}$ the number of degrees of leptons, $\delta_\ell$ the heavy-light charged lepton mixing in Eq.~(\ref{eqn:Lmix2}), and $\delta_{S}$ the charged scalar mixing~\cite{Dev:2016qbd} (without the assumption of lepton-specific structure of the scalar sector).
By adjusting the mixing parameters $\delta_{S}$ and $\delta_\ell$, we can make $N_2$ decay after $T_F$.

Now we calculate the relic density of $N_2$ (mostly governed by the off-resonance annihilation $N_2N_2\to $ SM fields), which will determine the extent of dilution. We find the number density of $N_2$ (normalized to the entropy density $s$)
\begin{eqnarray}
Y_{N_2} \ \simeq \ \frac{M_{N_2}}{\delta_{N_2} T_{N_2}}
\end{eqnarray}
where $\delta_{N_2}=\frac{2\pi^2g_*}{45}\frac{M^3_{N_2} \langle \sigma v \rangle }{H(M_{N_2})}$. Using for instance the scalar channel with $\langle \sigma v \rangle \simeq \frac{3\lambda^2f^{\prime 2}}{1024 \pi M^2_{N_2}} \langle v^2 \rangle$, we find $Y_{N_2}\simeq 10^{-2}$ for $M_{N_2}\sim 10$ PeV.

The dilution factor is then calculated by equating the energy density before and after the decay:
\begin{eqnarray}
Y_{N_2}M_{N_2} s_{\rm before} \ = \ \frac{3}{4}s_{\rm after}T_{N_2} \,.
\end{eqnarray}
The dilution factor is then given by $d = {s_{\rm after}}/{s_{\rm before}}$, i.e.
\begin{eqnarray}
d \ = \ \frac{4}{3}~\frac{Y_{N_2}M_{N_2}}{T_{N_2}} \,.
\end{eqnarray}
With mixing parameters $\delta_S \simeq 0.1$, $\delta_\ell \simeq 0.01$ GeV, $\lambda \simeq 0.03$ and $y_e^{(\prime)} \simeq 0.3$, we can get a dilution factor as big as $d\sim 10^6$, which is adequate to give the right relic density of $N$ for $M_N$ up to a PeV or so, as can be seen from Fig.~\ref{fig:uni}.

\section{Direct and indirect detections and collider searches} \label{sec:4}

As a Majorana DM candidate, the RHN has both spin-independent (SI) and spin-dependent (SD) interactions with nuclei, which are mediated by the scalars and neutral gauge bosons, respectively.

The amplitude due to heavy scalar exchange is suppressed by its large mass, thus the SI scattering cross section is dominated by the SM Higgs contribution
\begin{eqnarray}
\label{eqn:sigmaSI}
\sigma_{\rm SI} \ = \
\frac{\lambda^2 \mu^2 M_N^2}{2\pi m_h^4 w_{R}^4 }
\left[ Z f_p^{} + (A-Z) f_n^{} \right]^2
\end{eqnarray}
where $\mu$ is the reduced DM-nucleus mass, and $f_{p,n}$ the effective Higgs-proton/neutron couplings.
A  characteristic feature of our model is that $\sigma_{\rm SI} \propto M_N^2$, which originates from the dependence of Yukawa coupling on the DM mass $f' \propto M_N$. As shown in Fig.~\ref{fig:dd1}, when the right-handed scale $w_R$ goes higher, the scalar and gauge mixings are decreased and the scattering cross section $\sigma_{\rm SI}$ also gets smaller. In this plot we adopt the benchmark values of $v_R = w_R =$ 1, 3 and 10 TeV, the gauge coupling $g_R = g_L$ and the quartic coupling $\lambda = 1$.
The colorful bands are due to the sizable uncertainties of effective couplings $f_{p,\,n}$. The most stringent current direct detection limits come from LUX~\cite{Akerib:2016vxi} (with comparable limits from PandaX-II~\cite{Tan:2016zwf}), which rule out the lighter RHN DM mass range, if the DM relic density is set to be the observed value (the gray contours). When the collider limits on $Z_R$ mass are also taken into consideration (with the dashed gray lines excluded in Fig.~\ref{fig:dd1}), we can set more stringent lower limits of a TeV or so on the DM mass. We show also the projected limits from XENON1T with exposure values of 2 and 20 ton$\cdot$year~\cite{Aprile:2015uzo} and the LZ experiment~\cite{Akerib:2015cja} with orders of magnitude improvement in the SI scattering cross section limits, which can constrain the DM mass $M_N$ and right-handed scale $w_R$ up to the 10 TeV scale in near future experiments.

\begin{figure}[t!]
  \centering
  \includegraphics[width=0.6\textwidth]{dd_SI.pdf}
  \caption{Predictions for the SI DM-nucleon scattering cross sections as functions of DM mass $M_N$ with the gauge coupling $g_R = g_L$ and the RH scale $w_R = 1$, 3 and 10 TeV. The colorful bands are due to the sizable uncertainties of effective DM-nucleon couplings $f_{p,\,n}$. We show also the current upper limits from LUX~\cite{Akerib:2016vxi}, as well as the future reaches of XENON1T~\cite{Aprile:2015uzo} and LZ~\cite{Akerib:2015cja}. The gray curves correspond to the parameter space producing the observed relic density $\Omega h^2 = 0.12$ (with the dashed part excluded by direct collider searches of $Z_R$ in the dilepton channel).}
  \label{fig:dd1}
\end{figure}

As for the SD scattering, it is mediated at leading order by the $Z$ and $Z_R$ bosons, both of which are suppressed by the small $Z - Z_R$ mixing angle $\zeta_Z$.
When the collider constraints on $M_{Z_R}$ are taken into consideration, the $Z - Z_R$ mixing is so small that even with the future LZ limits it is rather challenging to test the model in the SD channels.

In the early universe, the RHN DM annihilates into the SM particles, e.g. $W^+ W^-$, $\ell^+ \ell^-$ and $q \bar q$, which could emit  energetic gamma-rays. Thus the RHN DM can also be probed by the Fermi-LAT gamma-ray observations. Also DM annihilation injects energy into the thermal bath in the early universe, thus the annihilation cross section could also be constrained by the Planck data of the cosmic microwave background (CMB). However, limited by the small scalar and gauge mixing angles ($\zeta_S$ and $\zeta_Z$), these indirect detections do not put additional constraints on the currently allowed model parameter space with the observed relic density.

As in usual thermal DM models, the RHN DM can be pair-produced at high energy hadron colliders, with monojet, mono-$h$, mono-$W/Z$ and mono-photon signatures. However, suppressed again by the small mixing parameters, none of these channels could effectively probe our model at the LHC. It might be helpful to check some specific parameter regions at future higher energy colliders, such as FCC-hh and SPPC.

\section{Decaying RHN DM and IceCube PeV neutrinos}

In the model discussed in Section~\ref{sec:model}, the SM charged leptons $e_R$ do not mix with their heavy partners ${\cal E}_L$, thus the lightest RHN is stabilized by the automatic $Z_2$ symmetry. If we add the following term to the Lagrangian
\begin{eqnarray}
\label{eqn:Lmix2}
{\cal L}_{\rm mix} \ = \ \delta_\ell \bar{\mathcal{E}}_Le_R + {\rm H.c.} \,,
\end{eqnarray}
to explicitly break the $Z_2$ symmetry (albeit softly), then the lightest RHN can decay into SM lepton and $W$ boson through the loop mediated $W - W_R$ mixing, i.e. $N \to W^\pm \ell^\mp$. This raises the interesting possibility of explaining the IceCube PeV neutrinos~\cite{Aartsen:2015zva} when we set $M_N \sim$ few PeV~\cite{Dev:2016qbd}. However, the two-body decays are disfavored by the IceCube data, as the neutrino spectrum is flatter than required~\cite{Dev:2016qbd}.

To fit the IceCube neutrino data, we promote the scalar sector to that of a lepton-specific two Higgs doublet model (2HDM) in both the SM and heavy sectors, with the Yukawa couplings given by
\begin{eqnarray}
\label{eq:Lyukawa}
- \mathcal{L}_Y & \  \supset \ &
 y_{u}  \bar{Q}_L \tilde{\chi}_{L,q} u_R
+ y_{d}\bar{Q}_L  \chi_{L,q} d_R
+ y_{\ell} \bar{\psi}_L  \chi_{L,\ell} e_R
\nonumber \\
&& + y'_{u}  \bar{\cal Q}_R \tilde{\chi}_{R,q} {\cal U}_L
+ y'_{d}\bar{\cal Q}_R  \chi_{R,q} {\cal D}_L
+ y'_{\ell} \bar{\Psi}_R  \chi_{R,\ell} {\cal E}_L
+ {\rm H.c.} \,,
\end{eqnarray}
where the electroweak VEV $v_{\rm EW} = \sqrt{v_{L,\ell}^2 + v_{L,q}^2}$ with $v_{L,\ell} = \langle \chi_{L,\ell}^0 \rangle$ and $v_{L,q} = \langle \chi_{L,q}^0 \rangle$. When the VEV ratio $\tan\beta = v_{L,q} / v_{L,\ell} \gg 1$, then the singly-charged scalar is predominantly from the lepton doublet, i.e. $\chi_L^\pm \simeq (\chi_{L,\ell}^\pm - \cot\beta \chi_{L,q}^\pm)$, and its hadronic decays are highly suppressed by $\tan\beta$. Mediated by the mixing of $\chi_L^\pm$ with its heavy partner $\chi_R^\pm$ which couples to the DM, we can have three-body decay of DM, i.e. $N \to \ell^+ \ell^- \nu$, which can successfully fit the IceCube data~\cite{Dev:2016qbd}.

\section{Conclusion}

In summary, we have discussed the phenomenology and cosmology of a new TeV-scale RHN DM candidate in the context of an $SU(3)_c\times SU(2)_L\times SU(2)_R\times U(1)_{Y_L}\times U(1)_{Y_R}$ model, where we introduced an $SU(2)$ analog of the electroweak interaction and matter contents but with a common QCD. After symmetry breaking, there is an automatic $Z_{2}$ symmetry in the leptonic sector that guarantees the stability of the lightest RHN, which plays the role of cold DM in the universe.
The DM relic density and direct detection constraints imply a lower limit of order 1 TeV for the RHN DM. We have also discussed a dilution mechanism which can push the RHN dark matter mass to the multi-PeV range (beyond the conventional unitarity limit) so that together with a weak breaking of the $Z_2$ symmetry, the RHN DM can in principle explain the PeV neutrinos observed at IceCube.

\section*{Acknowledgment}
We thank Shmuel Nussinov for discussions and comments. This work of B.D. was partly supported by the DFG grant RO 2516/5-1. The work of R. N. M. is supported by National Science Foundation grant no. PHY1620074. Y. Z. would like to thank the IISN and Belgian Science Policy (IAP VII/37) for support.


\section{The Early Internet}
\label{sec:c1}
\setcounter{paragraph}{0}

This class includes those protocols that were designed in the context of
the early Internet, roughly from 1960 -- 1988, where attacks had yet to
be considered and therefore protocols were designed without security
considerations.  The paper by David Clark about ``The Design Philosophy
of the DARPA Internet Protocols''~\cite{clark1988design} does not even
contain the term security even though availability in the sense of
survivability is a major goal. After all, the main goal of the Internet
was to interconnect existing networks with the implicit assumption that
all participants worked towards the common goal of communication.

As a result attacks were not yet common. So, the need for security
either did not exist or was extremely limited. Towards the end of the
era, attacks against operating systems became more prominent and the
first major Internet worm, namely the Morris worm,
was let loose~\cite{orman2003morris,spafford1989internet}.

Most popular protocols from that era have been updated to remain usable in
today's hostile Internet. However, this does not remove all \mk
traps. Today many still have artifacts of  their design for a friendly
Internet.

Thus, the threat model of this class is: ``weak attacker'' with ``\good''.  The
representative protocols we examine are: SMTP and DNS.
Other protocols in this class include: TFTP, FTP, Finger, rexec, Chargen, NIS, RIP, NTP,
WHOIS, Ident, XDMCP/X11, Syslog, rsync and IRC.

\subsection{Example Protocols}
\setcounter{paragraph}{0}

\input{ftp}

\input{tftp}

\input{dns}

\input{smtp}

\input{rip}
\input{nis}

\subsection{Discussion---\early}

A common \mk trap in this class is the assumption that neither client
authentication nor encryption is needed as the services are in a trustworthy
environment. Indeed, access without authentication is considered a feature
(FTP, SMTP, and DNS). Other abuses of \mk are stateless amplifications attacks
(TFTP, DNS) where the root cause is that the server sends data without checking
if the client wants it.

Based on these observations one would presume that protocols in this class have
seen the end of their live cycle. However, almost all of the above protocols
are still very popular.  The reason is (a) the Internet relies on the services
(DNS, SMTP) (b) their convenience (FTP), (c) the fact that there is no good
alternative (TFTP), and (d) the service happens to be running and is a legacy
service. Worse, the implementation of, e.g., TFTP requires a small code base which
makes it common in millions of customer premise equipment (CPE).
Indeed, these protocols are unlikely to disappear as they are the
foundation of the Internet.

The reason why such services are still in operation is twofold: Either it
is presumed possible to hide the services behind firewalls (TFTP, NIS, RIP) or
work on alternative protocols has started, but these protocols are not yet in
Internet-wide use (DNS, SMTP).  But, \mks occur if either the firewall fails or
the protocols are not used as originally designed.

The first major security incident which exploited a \mk was an email
amplification attack - namely the Morris worm in
1988~\cite{spafford1989internet}. At about the same time, the community started
to realize that major \mks can occur, see RFC1222~\cite{rfc1222} and
RFC1223~\cite{rfc1223} that ``provide guidance for vendors, implementors, and
users of Internet communication software''.

\section{Emerging Threats}
\label{sec:c2}
\setcounter{paragraph}{0}

Security incidents such as the Morris worm changed the way that Internet
protocols are perceived. Instead of designing them for the Internet at large,
they became explicitly designed with firewalls in mind. Thus, network firewalls,
more precisely packet filters~\cite{chapman1992network}, became the typical way
of fencing off network services.

Bellovin and Cheswick~\cite{bellovin1994network} state that the motivation for
Network Firewalls is: \emph{``Computer security is a hard problem. Security on
networked computers is much harder. Firewalls (barriers between two
networks), when used properly, can provide a significant increase in computer
security.''}  In addition, the approach from 1988 onwards is, according to
Bellovin and Cheswick~\cite{bellovin1994network}: \emph{``Everything is guilty
until proven innocent.  Thus, we configure our firewalls to reject
everything, unless we have explicitly made the choice - and accepted the risk
- to permit it''}.

Protocol designers find network firewalls to be a convenient way to handle
security. In their minds, firewalls enable them to basically ignore security
threats as they presume that the firewall rejects everything that is
``untrusted''. The design assumption of most protocols is that since the
attacker is not strong enough to get past the firewall the protocol itself can
be designed for a trusted environment.

However, as stated by Wool~\cite{wool2004quantitative}: \emph{``The protection
  that firewalls provide is only as good as the policy they are configured to
  implement. Analysis of real configuration data shows that corporate firewalls
  are often enforcing rule sets that violate well established security
  guidelines.''} His conclusion is to keep firewall configurations simple
but efficient to avoid \mk.

Thus, the threat model for this class is: ``weak attacker'' with
\perfect.  The representative protocols we take a closer look
at are: NetFlow, DHCP, and, iSCSI. Other protocols in this
class include: SNMPv2, Munin, NFSv3, Wake on Lan, Remote DMA, NBD, rsyslog, SCADA, early versions of
CIFS/SMB, and Mapping of Airline Traffic over Internet Protocol (MATIP).

\subsection{Example Protocols}
\setcounter{paragraph}{0}

\input{netflow}

\input{dhcp}

\input{snmpv2}

\input{munin}

\input{nfsv3}

\input{iscsi}

\subsection{Discussion---\emerging}

The base assumption of all protocols/services in this class is that the local
LAN is safe. Thus, a common misconception is that they can be used with
``convenient'' security settings. This often leads to major security incidents
when the fencing mechanisms fail. This is the major \mk trap for all protocols
in this class.

NetFlow is a blatant example of the low security considerations within this
class. Its security concept  relies entirely on fencing. DHCP goes even further:
first anyone can run a rogue DHCP server and second engineers think about DHCP
as a link layer protocol. SNMPv2 is one of the protocols in this class that
first added security but then reduced it. NFSv3 does do authorization using
OS ACLs, but without authentication. This means that anyone can impersonate
anyone.  While iSCSI, in principle, supports authorization and authentication
some deployments do not enable it as iSCSI should be restricted to the storage
network and, if used as boot device, is difficult to supply the clients with
secured credentials for the iSCSI volume. However, if fencing breaks down this
is a major \mk as large amounts of sensible data are leaked.

However, the assumption that everything can be fenced in does not necessarily
hold as specifying security policies is difficult and realizing them in
a firewall is rather difficult and prone to
errors~\cite{mayer2000fang,al2003firewall,cuppens2005detection,yuan2006fireman,garcia2013management}.
Among the complications are that the designer of the security policies
are not necessarily the ones that configure the firewalls and those are not
necessarily the ones that deploy the network services. Moreover, updating and
maintaining such rules is quite error prone. This opens up the network
service for all kinds of attacks that bypass firewalls or access services that
are thought to not be reachable from the Internet.

Other means of fencing include: (a) not connecting the service to the Internet
at all (air gap) (b) VLANs and sub-networks (c) Virtual routing and forwarding
(VRF).  But, there are known attacks to all of them. Examples of how firewalls
are circumvented via VPNs, hidden dialups/UMTS and other covert channels are
described in the Maroochy water breach
discussion~\cite{slay2008lessons}. Stuxnet~\cite{falliere2011w32} is the prime
example for bypassing an air gap.  One example for broken VRF is accidentally
announcing a BGP full table into the VRF engine.  Overall, the industrial lore
states, from the Security Issues and Best Practices for Water/Wastewater
Facilities~\cite{hayes2013security}: \emph{``Industrial networks are often
  shared with the business side of the operation. VLANs, sub-networks,
  firewalls all help to create a layer defense, but are not impervious.''}.

This is  particularly the case for services that were first envisioned for
enterprises and  then commonly used in Small Office/Home Office (SoHos)
and home networks. In these settings security by default configurations are
essential as the users often lack the knowledge and means to properly address
security and network challenges.

\section{Complex Security Solutions}
\label{sec:c3}
\setcounter{paragraph}{0}

At the end of the 20th century the awareness that firewalls were not ``the''
security solution became prominent. For example, RFC3365~\cite{rfc3365} dated
2002 states: \emph{``History has shown that applications that operate using the
  TCP/IP Protocol Suite wind up being used over the Internet.  This is true
  even when the original application was not envisioned to be used in a ``wide
  area'' Internet environment.  If an application isn't designed to provide
  security, users of the application discover that they are vulnerable to
  attack.''}

As a result, protocol designers realized that (a) there was a need for improved
protection architectures, e.g., the work on SANE~\cite{casado2006sane} or
DoS-limiting network architecture~\cite{yang2005limiting}, and (b) that
security had to be an essential feature of future protocols and services.
Moreover, just adding another component to ensure security to existing
protocols, e.g., firewalls, did not suffice.  This fits the increased need for
security in the society  due to the increasing economic relevance of the
Internet~\cite{mahadevan2000business}.

At the same time the diversity of the scenarios also increased with home users,
SoHos, enterprises, infrastructure providers, company mergers and splits,
etc. Indeed, road worriers started to appear.  As a result,
more assets were at stake which had to be accessible in many different ways. Thus,
versatile security solutions to model complex organizational
structures, e.g., via role-based access control (RBAC), were needed.

Indeed, the Danvers Doctrine~\cite{rfc3365} stated that the \emph{``IETF should
standardize on the use of the best security available''}. Thus, the threat
model for this class is: ``strong attacker'' with ``\perfect''.  The representative
protocols we take a closer look at are: IPP, SNMPv3, and IPFIX.  Other
protocols in this class include: LDAP-ACL, NFSv4, AFS, Postgresq, FTPs, RADIUS/WPA2Enterprise, s/MIME encryption,
SSL/TLS, PGP, and seLinux, as an example from system security.

\subsection{Example Protocols---\complex}
\setcounter{paragraph}{0}

\input{ipsec}

\input{ldap}

\input{ipp}

\input{nfsv4}

\input{snmpv3}

\input{ipfix}

\subsection{Discussion---\complex}

The common design of all protocols within this class is that they are designed
according to the Danvers Doctrine~\cite{rfc3365}. Therefore, they all offer full CIA support.
Unfortunately, when looking at the deployment base, we either find few indications
of actual use of the protocol or that the deployed instances do not utilize or implement
the full CIA support.

Among the reasons are difficult setup (LDAP, NFSv4) or limited
perceived benefit of latest version of the protocol (NFSv4, SNMPv3).  Also, they
are often used within the SoHo, rather than the enterprise, where there is a lack
of required security infrastructure (IPP without Kerberos). Furthermore,
implementations do not support required protocol security features
(IPFIX). Furthermore, third party documentation may recommend simpler
solutions, e.g., Postgres.

Another aspect is that the system administrator and the IT security
professionals are typically not the same person,
e.g.,~\cite{botta2007towards,furnell2009integrated}.  Moreover, these systems
come with substantial complexity which leads to many \mk traps. For example,
Xu et al.~\cite{xu2013not,xu2015hey} in their papers \emph{``Do Not Blame Users
  for Misconfigurations''} and \emph{``Hey, You Have Given Me Too Many Knobs!
  Understanding and Dealing with Over-Designed Configuration in System
  Software''} point out that major causes of today’s system failures are
\mks due to complexity. However, it is not necessarily the user or
the system administrator who is to blame, but rather the inherent complexity
and mismatch of the tools~\cite{haber2007design,barrett2004field} as well as
poor usability for system operators~\cite{xu2013not,xu2015hey}.

Given the above complexity, let's review what might or might not
motivate a system operator to deploy the latest secure protocol suites,
see, e.g., the discussion of West as well as Scheier in their papers on
\emph{``The psychology of
  security''}~\cite{west2008psychology,schneier2007psychology}: (a) No
or little reward for secure behavior. Indeed, there are hardly any
monetary incentives for deploying the secure versions. Some claim that
such incentives might change this~\cite{greenwald2004user}.  (b) The
misconception of operators that there is a low risk of being attacked.
(c) The ``laziness'' of the operator that wants to get the main service
working first and then worry about security if there is time left.  (d)
The time pressure by management that forces the operator to get a
service working in no time.  (e) The presumption that no one is
likely to get caught for not deploying the secure version of the
service. (f) The maintainability of the complex security infrastructure.

\section{A new Simplicity}
\label{sec:c4}
\setcounter{paragraph}{0}

The inherent complexity of protocol suites of the previous class provided
the motivation for trade-off based security.  This class is
about ``strong attackers'' and ``\good'' security.
As noted by Bruce Schneier~\cite{schneier2007psychology}: \emph{Security is a
  trade-off. This is something I have written about extensively, and is a
  notion critical to understanding the psychology of security. There's no such
  thing as absolute security, and any gain in security always involves some
  sort of trade-off.}

The protocol designs in this class must be seen in the context that we now
have clouds as well as many start-up companies with various (mobile)
applications. Indeed, the Internet is experiencing yet another growth
explosion in terms of services~\cite{armbrust2010view,pallis2010cloud}.  In
terms of infrastructure, we are now in a ``world of HTTP everywhere'',
virtualization, the cloud, large scale as well as microservices architecture,
and configuration orchestration.

Let us consider Internet application developers. Among the easiest ways
to develop new applications is to do it in the cloud using a
microservice architecture. They can rely on ``Node.js'' or
similar programming languages and reuse existing code. The reuse of
existing code has been made easy by the equivalent of appstores. As
transport protocol they will most likely use HTTP/HTTPs.
Moreover, the application grows as the feature sets and/or user
base increases. A common observation is that the security review of such
services is often lacking and the assumption is that it is possible to
fence the service in a private cloud as it is just another Web service.

With ``simplicity'' we refer to the security concept rather than the feature
sets of the protocols or, rather, protocol suites.  The threat model for
this class is: ``strong attacker'' with ``\good''.  The representative
protocols/protocol suites we examine are: Telnet, key-value
stores, VNC, and the many incarnations of (HTTP/Socket) APIs. Other protocols
in this class include: PulseAudio's and Systemd's internal protocols as well as
control protocols for tools such as Nessus, Aircrack, etc. Since most of these
use HTTP as transport layer protocols the same \mk traps apply as discussed in
the API subsection.

\subsection{Example Protocols}
\setcounter{paragraph}{0}
\input{telnet}

\input{kv}

\input{vnc}

\input{apis}

\subsection{Discussion---\simplicity}
In this class, we often do not have a single protocol but concepts that are realized by
different protocols that all suffer from the same \mks, e.g., key-value stores
and APIs. Overall, we observe a clear trend towards using HTTP as
application layer protocol, likely because HTTP allows middlebox
traversal~\cite{qazi2013simple}. In theory, this opens up the possibility of
''just securing HTTP''
rather than having to secure a large number of Internet
protocols~\cite{richter2015distilling}.  Still, the problems of \mk
remain. Even if an API uses SSL for encryption, it can still be abused
by an attacker~\cite{breen2015java} to disclose information.  The origin
of this trend is the need for complex, yet easy to deploy services.

Apart from delegating security issues to HTTP these modern services again rely
on fencing.  During software and system development, the main focus is on
getting the service ready and not necessarily on security.  Hence,
\emph{``\lbrack{}...\rbrack~Its operation environment is assumed to be
  non-hostile~\lbrack{}...\rbrack''} as stated in the Amazon Dynamo
paper~\cite{decandia2007dynamo}.

The underlying misconception is that services can be securely fenced off as
they are only used within ``internal systems''.  That this can lead to \mks has
already been shown in previous discussions.  Nevertheless, many recent security
incidents have lead to prominent examples of data leakage (key-value stores,
APIs)~\cite{binaryedge2015a}.

The motivation for delegating security to a fenced environment is the notion
that security without fencing is a complex and time consuming task, impossible
to achieve, and making the (backend) services unusable. Hence, the spirit
during development follows the start-up culture, which includes reusing available
protocols as they are (Telnet/VNC).

Fencing techniques have advanced as well, and since 2013 include the
concept of containers~\cite{kim2013practical}. A common \mk is captured by the
following idea: ``If we put a service in its own container in its own dedicated
VM in its own VLAN behind a firewall nothing can happen''. However, since
services have to be reachable they have to allow some access. This access often
turns out to be the entry point for attacks.

Containers, e.g., Docker, are a deployment and testing mechanism.  The
motivation is that traditional means of software distribution do not scale
to the cloud as traditional testing/release procedures do not fit the rapid
development cycle. This often leads to monolithic deployment
of formerly modular software components. This is unmanageable if some component
has to be updated, e.g., to patch a security hole. Furthermore, containers
usually come preconfigured which adds additional \mk traps.

Due to their experience with \complex several developers state that one should
not be too strict about security and that security is ``in the way'' of
innovation. This goes as far as e.g. Ren et al.~\cite{ren2012security}
claiming that: \emph{``Security and privacy is one fundamental obstacle to cloud
computing's success.''}.

Old mistakes are redone as the default assumption of the software
developer is again ``this is an esoteric scenario and not the intended use
case''.  APIs may release more information than
intended~\cite{fiebig2013grindr,polakis2015s}.  Moreover, the cloud adds the
complexities of multi-party trust and the need for
mutual auditability~\cite{chen2010s}.  Additionally, developer guidelines with
a focus on security are hard to find even if they exist.

Overall, we note that, after having had too complex security and unusable systems,
we are now in a world with easily deployable solutions. However, security
is often outsourced. This results in many \mk traps.

\section{Summary}
\label{sec:conclusion}
\input{tabelle-full}

Our systematization of \mk prone Internet protocols and services
is based on assumptions about the attackers---weak vs.\ strong
attacker---as well as security trade-offs---\good vs.\ \perfect---in the protocols.
We find that \mk prone Internet protocols and their services fall into one of our four
classes: \early, \emerging, \complex, and \simplicity.

We observe that protocol design and service development have come full circle with regard to
security. In the sense that initially the Internet was a cooperative
environment, see \early. Once it was realized that the Internet was
hostile it was presumed that it was possible to fence of services, see
\emerging. However, attackers are getting stronger and assets more valuable
and, thus, there is the attempt to get security ``right'', see \complex.  The
drawback is complexity and, thus, we complete the circle back to a simple
security model in a
presumed friendly environment guaranteed by enhanced fencing mechanisms, see
\simplicity. Overall, we find many \mk traps in all of the above classes.

Fencing is seen as a major security solution and often used as only barrier
protecting major assets. However, fencing is a major \mk trap in itself. After
all, with regards to fencing there is the statement from
RFC3365~\cite{rfc3365}: \emph{``History has shown that applications that
  operate using the TCP/IP Protocol Suite wind up being used over the
  Internet. This is true even when the original application was not envisioned
  to be used in a “wide area” Internet environment.''}

We observe that protocol/service designers are clearly forced from one
extreme---full but too complex security---to the other extreme---hardly any
security but easily deployable software that works ``out of the box''.  Indeed,
our observation is that operators get frustrated if the software does not behave
as it should or prevents them from doing what they want to do.  Moreover, for many
decision makers, security is not an end in itself but it is a cost factor that they
``also have to take care of''---if it cannot be avoided. Yet, most
often a security incident proves to be more costly than proactive security
considerations would have been.

\subsection{Lessons Learned}
\vspace{-0.2cm}
Besides these observations, we compile a set of action points and
requirements protocol designers MUST consider when they
create new or update old protocols.

\noindent
\Early: The major lesson from this class is that security requirements and
environments change. However, this class also demonstrates that such issues can
be tackled. Hence, \textit{\textbf{when updating a protocol, one MUST purge
    problematic use-cases and design choices.}} Only then can appeals for
fixing bad configurations combined with sanctioning of insecure practices lead
to improved overall security (see, e.g.,~\cite{jung2004empirical}
and~\cite{kuhrer2014exit}). While the community succeeded with SMTP, the
Internet still suffers from, e.g., DNS and NTP amplification attacks. In
addition, other protocols from this era still linger and urgently
require revisiting.

\noindent
\Emerging: Given that the non-hostile Internet is gone, a new paradigm
emerged. Instead of adjusting the protocols to the new insecure environment,
the environment is re-defined to be fenced. Thus, the assumption is that the
service is behind a firewall or that lower layers offer security guarantees.
Yet, it is common knowledge that firewalls tend to fail eventually and lower
layers do not hold up to their promises. Thus, \textit{\textbf{when designing a
    protocol, one MUST not assume that it will only be used in the environment
    it was designed for.}} Moreover, \textit{\textbf{when designing a protocol,
    one MUST include authentication, authorization and confidentiality
    preserving methods}}.

\noindent
\Complex: Here the community tried to address some of the above
recommendations. However, the resulting protocols come with other
complications.  Security features designed for an enterprise setup may not be
appropriate in SoHo scenarios, e.g., recall IPP. IPSec is so complex that it is
not in widespread use. Moreover, implementations do not necessarily
interoperate.  In an attempt to ensure good cryptographic algorithms, SNMPv3
and SSHv1 specified algorithms that were good then but not necessarily
now. Hence this class provides us with the following three lessons.  First,
\textit{\textbf{when designing a protocol, one MUST ensure that the security is
    scalable.}} Scalable in the sense that it is applicable to large as well as
small setups. Even the simplest setup should provide confidentiality,
integrity, and availability by default. Second, \textit{\textbf{when designing
    a protocol, one MUST keep it simple and concise}}, to allow multiple
parties to implement interoperable solutions. Third, \textit{\textbf{when
    designing a protocol, one MUST not mandate the use of specific ciphers but
    one MUST exclude plain and weak algorithms}} since cryptographic algorithms
become obsolete over time.

\noindent
\Simplicity: Overwhelmed by the complexity of the previous protocol generation
a new protocol design trend emerged. Protocols become simple again, and
designer focus on getting things done. New technologies, such as ``Cloud'' and
``SDN'' also bring new paradigms. We find that large enterprises develop
protocols very similar to those of the era of emerging threats while ignoring
lessons learned often for the sake of performance. It works well for the
designed environment, e.g., large enterprises where the perimeter is secure,
but fails in different settings.  The concept of ``everything over HTTP'' leads
to ``protocols'' which ignore and/or misuse basic concepts such as
authentication and in particular authorization. In addition, we find that often
new actors, e.g., the automotive industry, adapt IP based technologies and
re-do old mistakes.  Hence, the most important takeaway from this class is that
\textit{\textbf{when designing a protocol, one MUST take past lessons into
    account}}. While this sounds simple history tells us it is not. Indeed,
almost all \mks pointed out by this survey are covered in even the most basic
security textbooks. Yet, they remain common and repeatedly cause major data
leaks and/or outages. Thus, the prime message of this survey is to finally
apply what we have learned.

\noindent
\textbf{\textit{General Observations:}}
Protocol designers MUST be strict in requiring all
security features from implementations and this must be reflected in the RFCs
or related standards.
To advance the use of TLS, a decent infrastructure, e.g.,
DANE~\cite{rfc6394,rfc6698} is necessary.
If such an infrastructure is unavailable encryption should at least be performed
opportunistically~\cite{Ylonen1996,RothSR2005}.

Opportunistic encryption raises the question of usability.
Usability has to become a key part of the protocol design process: The goal has to be
to make the protocol secure while designing the system such that
it is simple to comprehend and use. The correct way is either the only
way or at least the easiest way~\cite{balfanz2004search,RothSR2005,bernstein2012security}.

Good examples of such design practices exist in the context of user centric
protocols, e.g., SSH~\cite{Ylonen1996} and the large set of encrypted (mobile)
messaging protocols~\cite{7163029}.  The rise of the latter is motivated by
the---emotional---demands of end-users~\cite{kraus2015analyzing} and
professionals~\cite{mcgregor2015investigating} for easy but secure
communication. Important security features include strong mutual authentication
and opportunistic encryption. The same kind of protocol design is needed for
all Internet protocols and, in particular, those used within the infrastructure.

\section{Introduction}

Security incidents involving Internet services have become regular
events.  Examples include: (a) disclosures of information, e.g.,
petabytes of personal data stored in unprotected key-value stores -
NoSQL databases ~\cite{mongodbsec,binaryedge2015a}.  (b) Unauthorized
access via the Internet to systems, e.g., supervisory control and data
acquisition systems (SCADA)~\cite{meixell2013out} which are used to
control systems which range from light installations to oil platforms.
(c) Undesired publication of information, e.g., health data from the
United Kingdom on an HTTP root~\cite{wired2014a}, or an UEFI signing key
on an internal FTP server which was available via the
Internet~\cite{caudill2013a}.

While programming vulnerabilities are well-studied,
e.g., see~\cite{mcgraw2006software,mcgraw2004software}, insufficient attention
has been paid to poorly designed and hard to configure protocols.  We
focus on protocol security practices with their varying na\"ivete,
complexity, and weaknesses.  In the context of this paper, we use the term
protocol to refer to transport and application layer communication
protocols.  We use the term service to refer to a deployed instance that
is offering the service associated with the protocol.

Indeed, among the root causes of the above severe incidents are \mks.
While this is, in principle, well known, e.g.,~\cite{cuppens2005detection,xu2013not},
to date, the main and only explanation has been human error. We claim
that there are more fundamental reasons for such \mks which stem from
the design of the Internet's protocols themselves, the security
assumptions or configuration choices offered by protocols. These lead to
services which are prone to \mk.

Our study complements the multitude of individual incidents documented
in the scientific literature and the anecdotes in systems lore with a
macroscopic systematic survey of Internet protocols and their
corresponding services.  More precisely, we investigate which of the
underlying assumptions during protocol design lead to \mks during
service deployment.  We refer to this as \mk prone protocols/services.

In the context of this paper we consider the following security relevant
\mks. A service is subject to \mk if it is deployed on the Internet in such a
way that any of the three main security properties - confidentiality,
integrity, or availability (CIA) - can be tainted.

There are many reasons for \mks: (a) the operator does not follow best
practices regarding network settings by which the service is deployed, (b) the
operator does not use the default configuration settings leading to tainted
CIA, or (c) the operator uses the default configuration settings and they lead
to tainted CIA.

Given the newest Internet trends, services in the cloud, Internet of
Things including Industry~4.0, autonomous systems, e.g., self-driving
cars, and mobile applications, we expect even more diversity and
complexity and, thus, more security incidents. Considering the
link between mismanagement and
maliciousness~\cite{zhang2014mismanagement,liu2015cloudy}, many of these
incidents will involve \mks. Thus, we claim that a systematic review of
why \mk occurs is needed.

\textbf{Contributions:} We review the assumptions under which protocols have
been designed along two dimensions, (a) the assumed strength of the attacker -
weak vs.\ strong - and (b) the defense paradigm - good enough vs.\ perfect
security. By using these dimensions to group protocols we find four major
clusters, one in each quadrant.  We name these clusters \early for weak
attacker/good enough, \emerging for weak attacker/perfect security, \complex
for strong attacker/perfect security, and \simplicity for strong attacker/good
enough. The names capture the design essentials as well as the mindset of the
protocols in each of the classes. Furthermore, the names express how the
security mindset of protocol design evolved over time.  From this
systematization of \mk prone protocols we derive a set of specific action
items. To keep protocols secure and \mk resilient these must be consider when
introducing new or updating old protocol specifications.

\textbf{Structure:} This paper is structured as follows: We introduce our
systematization methods in Section~\ref{sec:method}. Next, we dedicate a
chapter to each of the four classes, Sections~\ref{sec:c1} to~\ref{sec:c4},
examining how and why protocols and services in the specific class are prone to
\mk. For each class we show its properties based on a few examples which we
discuss in detail. Each of these chapters concludes with a discussion which
summarizes our observations about the \mks within the class.  Finally, in
Section~\ref{sec:conclusion}, we provide design recommendations for future
protocols as well as deployed services, and end with concluding remarks.

\section{Systematization Method}
\label{sec:method}

Thousands of Internet protocols have been proposed, developed, and
deployed on the Internet; therefore an exhaustive analysis is beyond
the scope of this paper. Rather we extract essential features from a
subset of \mk prone protocols and use
these to derive our systematization.

\subsection{Example protocol selection}
Our choice of protocols is driven by the following considerations. First, we
choose protocols that are commonly used and/or are new and upcoming. Next, we
choose some were \mks can potentially have a large impact or those where
system lore states that they are easily \mked.  We augment this list by
protocols that capture corner cases.
From these we selected a set of protocols that are most iconic vor the relevant
class. Due to the size limitations of the work at hand, only a subset can be
introduced in detail and displayed in Table~\ref{tbl}.
We focus on the server, not client side. Thus,
pure end-user focused protocols as well as client \mks are beyond the
scope of this paper.

\subsection{Security relevant \mks}
If a service is deployed in such a way that its CIA is tainted because
of a \mk we call the \mk security relevant. There are three main reasons
for such \mks. The first is when the operator of the service does not
follow best common practice (BCP). The second is when the operator uses their
own configuration which taints the CIA of the service. The third is
when the operator uses the default configuration, but the CIA is still
tainted, likely due to incorrect defaults.

We refer to \mk prone protocols and services. But in the end it is the
service that is \mked, often facilitated by design choices in the
protocol. Examples for common \mks are that the service is deployed in a
network setting which deviates from the one for which it, or its
default configuration, was designed.

\subsection{Security guidelines for protocol design}

Request For Comments (RFCs) document Internet protocols and services. Since
1992, each RFC must address the topic of security, according to, IETF processes,
(RFC1311~\cite{rfc1311}, RFC1543~\cite{rfc1543}, RFC2223~\cite{rfc2223},
RFC7322~\cite{rfc7322}), which document what an RFC must contain. Indeed,
RFC1311~\cite{rfc1311} states: \emph{``All STD RFCs must contain a section that
discusses the security considerations of the procedures that are the main topic
of the RFC.''}

Over time, the community has realized that this statement by itself is
not sufficient and the specification of the security requirements have
gotten stricter, see RFC3552~\cite{rfc3552} from 2003, the Best Current
Practices for \emph{``Writing RFC Text on Security Considerations''}.
The goal of this requirement is to make all protocol designers and
implementers aware of possible security implications. Given that this
basic requirement existed in 1992, we conclude that the importance of
security has been recognized for at least 23 years.

\subsection{Review of security threats for protocols and services}

One of the motivations for including a security section in each RFC is to make
the protocol designer consider the following two questions: (a) against whom to
defend and (b) how to defend.

We find that protocol designers consider different kinds of attackers, ranging
from very weak to very strong.  The weak attacker is either
unskilled or is resource limited. The strong attacker is very skilled and has
all necessary resources in their hands.

Defining how to defend is more difficult as it depends on the eyes of
the beholder. Some argue that the cost of breaking security should be
larger than the value of the protected asset.  This goes back to
Pfleeger and Pfleeger~\cite{pfleeger2002security} and specifies that
one should put up a wall against threats at least high enough that most
attacks will not break the wall. Moreover, the wall should not cost more
than the protected asset. We call this the ``\good'' approach to
security. Others, especially the field of
cryptography~\cite{kramer2015cryptography}, follow the approach of
``\perfect''.  \Perfect refers to using every possible mean to achieve
security. We refer to these two approaches as the defense paradigm.

\subsection{Classification of protocols and services}

Thus, we have two-dimensions, namely, the capabilities of
the attacker and the defense paradigm. Using these dimensions
we classify our selected set of protocols and identify four major
clusters. These clusters correspond to the four quadrants of the two dimensional
space. We refer to them as: \early, \emerging, \complex, \simplicity.

\begin{description}
\item[Weak attacker - \good] ~\newline This class contains those
  protocols that are designed for a friendly, collaborative environment - the
  Internet when security was not yet a major concern. This class, in
  particular, contains those protocols that initially were designed
  under the assumptions that there is no attacker, or still carry artifacts from
  that idyllic time. Such an attacker is the weakest one possible.
  We refer to this class as \early.
\item[Weak attacker - \perfect] ~\newline This class no longer assumes that
  the environment is entirely friendly. Rather it recognizes that there are
  threats, but not yet by sophisticated attackers. However, since significant
  assets can be at stake, even attacks that are only theoretically possible are
  considered.  We refer to this class as \Emerging.
\item[Strong attacker - \perfect] ~\newline This class captures the
  protocols that consider security a necessity at all costs. As a result, the
  protocols in this class are designed to handle strong attackers and be safe
  against all, even theoretically conceived, attack vectors.
  However, as a result, they are often complex and hard to deploy, maintain, and
  difficult to use. We refer to this class as \Complex.
\item[Strong attacker - \good] ~\newline This class contains those
  protocols who's designers recognize that strong attackers exist but
  also value protocols that ``just work'' out of the box. Therefore, the
  designer does not try to defend the asset against every possible
  attack by reducing the attack surface.  In this class we see a
  conscious choice between security and operational ease, favoring the
  latter.  We refer to this class as \Simplicity.
\end{description}

Interestingly, when one considers when most protocols in each of the
above classes were designed, we find that Internet protocol designers
have started with protocols in the \early category, and moved to ones
from \emerging when they realized that the Internet was no longer
nice. However, while the core ideas did not change, the protocols were
hidden behind fences such as DMZs. Since this did not suffice, they
moved to \complex.  As these were hard to maintain or difficult to
use, we see a new trend towards \simplicity.

\subsection{Systematization}
\setcounter{paragraph}{0}

In Sections~\ref{sec:c1}--\ref{sec:c4} we take a closer look at each of the
above classes. For each class, we identify a set of representative protocols
which we analyze according to five sets of features.

\noindent{\bf{\Details:}}
Among the essential security features that protocols should support are
authentication, authorization, and use of encryption (TLS for transport layer
encryption).  We mark for each
protocol/service which of these features is (a) in common use (\yes), (b)
implemented but not commonly used (\no), (c) not implemented  (\na). If the
protocol does not support a security feature we leave the space blank.

\noindent{\bf{\Mk traps:}} We consider the possible \mk traps which a
protocol/service may have.  Under \textbf{NoAuth} we capture if (a)
authentication is not offered by the protocol, (b) typically not
implemented, or (c) typically not configured in the deployed
service. Under \textbf{Credentials} we note if the service is commonly
deployed with weak default credentials. Under \textbf{Artifacts} we note
if protocol features common at design time lead to \mks when used
today. With \textbf{Fencing} we note those cases that depend on
firewalling, etc. to ensure that they are not reachable from the
Internet.  We mark those protocols \textbf{NoUse} that are hardly deployed even
though they replace earlier protocols, e.g., prior versions, with major \mk traps.

\noindent{\bf{\Docs:}}
As \mks often occur due to poor technical support for operators, we
look closely at that for each of our representative protocols.
More precisely, we look at the documentation for securely deploying the
service and check if it is mostly (\no) or always (\yes)
misleading, lacking, too complex, or
otherwise insufficient.  Another common aspect that leads to \mks
are bad defaults.  But rather than looking at what can go wrong we check if the
defaults are always (\yes) or sometimes not ``sane'' (\no).  Sane in the sense that
they enable or enforce enabling the supported security features of the
protocol/service to ensure confidentially, integrity, and availability by default.

\noindent{\bf{\Pub:}}
Here we capture if problems that can lead to \mks discussed under \mk
traps or \docs are already well known either in the academic world or
the security community.  If it is known in the academic world, we refer
to a representative paper. If it is known in the community we note
approximately when it became part of the system engineering lore.

\noindent{\bf{\Usage:}} Next we try to estimate the number of systems,
or rather IP addresses, that offer the service/protocol under
discussion. We rely on different data sources, among them (a) publicly
available data sets or representative papers, (b)
zMap~\cite{durumeric2013zmap} scans by the authors, and (c) search results
from Shodan~\cite{bodenheim2014evaluation,shodan2015a}. Shodan is ``the
world's first search engine for Internet-connected devices''. While
Shodan does provide an estimate of the possible number of IPs offering a
service it is neither complete, covers all available
ports~\cite{bodenheim2014evaluation}, nor are all instances per se
vulnerable.


\section{Introduction}\label{sec:intro}
\vspace{-2mm}
DNN based acoustic models have been state-of-the-art for automatic speech recognition over the past few years~\cite{hinton2012deep}. While DNN input consists of multiple frames of acoustic features, the target output is obtained from a frame level GMM-HMM forced alignment corresponding to the context dependent tied triphone states or senones~\cite{young1994tree}. This procedure results in inefficiency in DNN acoustic modeling~\cite{jaitly2014autoregressive,senior2014gmmfree}.
Unlike the conventional practice, the present work argues that the optimal DNN targets are probability distributions rather than Kronecker deltas (hard targets). Earlier studies on optimal training of a neural network for HMM decoding provides rigorous theoretical analysis that supports this idea~\cite{bourlard1994remap}. Here, we propose a DNN based data driven framework to obtain accurate probability distributions (soft targets) for improved DNN acoustic modeling. The proposed approach relies on modeling of low-dimensional senone subspaces in DNN posterior probabilities.

Speech production is known as the result of activations of a few highly constrained articulatory mechanisms leading to generation of linguistic units (e.g. phones, senones) on low-dimensional non-linear manifolds~\cite{deng2004switching,king2007speech}. In the context of DNN acoustic modeling, low-dimensional structures are exhibited in the space of DNN senone posteriors~\cite{dighe2015sparse}. Low-rank and sparse representations are found promising to characterize senone-specific subspaces~\cite{dighe2016exploiting,luyet2016lrr}. The senone-specific structures are superimposed with high-dimensional unstructured noise. Hence, projection of DNN posteriors on their underlying low-dimensional subspaces enhances the DNN posterior accuracies.
In this work, we propose a new application of \textit{enhanced} DNN posteriors to generate accurate soft targets for DNN acoustic modeling.

Earlier works on exploiting low-dimensionality in DNN acoustic modeling focus on exploiting low-rank and sparse representations to modify DNN architectures for small footprint implementation. In~\cite{xue2013restructuring,sainath2013low} low-rank decomposition of the neural network's weight matrices enables reduction in DNN complexity and memory footprint. Similar goals have been achieved by exploiting sparse connections~\cite{yu2012exploiting} and sparse activations~\cite{liu2015neuron} in hidden layers of DNN.
In another line of research, soft targets based DNN training has been found effective for enabling model compression~\cite{hinton2015distilling,chan2015transferring} and knowledge transfer from an accurate complex model to a smaller network~\cite{price2016wise}. This approach relies on soft targets providing more information for DNN training than the binary hard alignments.

We propose to bring together the advantage of higher information content of soft targets with the accurate model of senone space provided by low-rank and sparse representations to train superior DNN acoustic models. Soft targets enable characterization of the senone-specific subspaces by quantifying the correlations between senone classes as well as sequential dependencies (details in Section~\ref{sec:why_soft}). This information is manifested in the form of structures visible among a large population of training data posterior probabilities. Potential of these posteriors to be used as soft targets for DNN training is reduced due to presence of unstructured noise. Therefore, to obtain reliable soft targets, we perform low-rank and sparse reconstruction of training data posteriors to preserve the global low-dimensional structures while discarding the random high-dimensional noise. The new DNNs trained with low-rank or sparse soft targets are capable of estimating the test posteriors on a low-dimensional space which results in better ASR performance.
We consider PCA (Section~\ref{sec:pca}) and dictionary based sparse coding (Section~\ref{sec:dlsc}) for generating low-rank and sparse representations respectively. Strength of PCA lies in capturing the linear regularities in the data~\cite{hutchinson2015sparse} whereas an over-complete dictionary used for sparse coding learns to model the non-linear space as a union of low-dimensional subspaces. Dictionary based sparse reconstruction also reduces the rank of the senone posterior space~\cite{dighe2016exploiting}.

\begin{figure*}[t]
\centering
\includegraphics[scale=0.076]{senone-posteriors}
\vspace{-2mm}
\caption{ \footnotesize Correlation among senones due to: (a) long input context and (b) acoustically similar root in decision trees. In (c), we show examples of DNN  posterior probabilities for a particular senone class (in blue barplots) which highlight low-dimensional patterns (green boxes) super-imposed with unstructured noise. PCA and sparse coding enable recovery of the underlying patterns by discarding the unstructured noise, and provide more reliable soft targets for DNN training. $K$ denotes the size of DNN outputs which is equal to total number of senones.}\label{fig:senone-posteriors}
\vspace{-5mm}
\end{figure*}
Experimental evaluations are conducted on AMI corpus~\cite{mccowan2005ami}, a collection  of recordings of multi-party meetings for large vocabulary speech recognition. We show in Section~\ref{sec:analysis} that low-rank and sparse soft targets lead to training of better DNN acoustic models. Reductions in word error rate (WER) are observed over the baseline hybrid DNN-HMM system without the need of explicit sparse coding or low-rank reconstruction of test data posteriors. Moreover, they enable effective use of out-of-domain untranscribed data by augmenting AMI training data in a knowledge transfer fashion. DNNs trained with low-rank and sparse soft targets yield upto 4.6\% relative improvement in WER, whereas a DNN trained with non-enhanced soft targets fails to exploit any further knowledge provided by the untranscribed data. To the best of our knowledge, significant benefit of DNN generated soft targets for training a more accurate DNN acoustic model has not been shown in the prior work.

In the rest of the paper, the proposed approach is described in Section~\ref{sec:theory}. Experimental analysis is carried out in Section~\ref{sec:analysis}. Section \ref{sec:conclusions} presents the concluding remarks and directions for future work.

\vspace{-2mm}
\section{Low-Rank and Sparse Soft Targets}\label{sec:theory}
\vspace{-3mm}
This section describes the novel approach towards reliable soft target estimation. We study reasons for regularities among senone posteriors and investigate two systematic approaches to obtain more accurate probabilities as soft targets for DNN acoustic modeling.
\vspace{-3mm}
\subsection{Towards Better Targets for DNN Training }\label{sec:why_soft}
\vspace{-2mm}
Earlier works on distillation of the DNN knowledge show the potential of soft targets for model compression and the sub-optimal nature of the hard alignments~\cite{hinton2015distilling,gillick2011don}. Although hard targets assign a particular senone label to a relatively long sequence of ($\sim$10 or more) acoustic frames, senone durations are usually shorter.
A long context of input frames may lead to presence of acoustic features corresponding to multiple senones in the input (Fig.~\ref{fig:senone-posteriors}(a)), so the assumption of binary outputs renders inaccurate.

In contrast, soft outputs quantify such sequential information using non-zero probabilities for multiple senone classes. Contextual senone dependencies arising in soft targets can be attributed to the ambiguities due to phonetic transitions~\cite{gillick2011don}. Furthermore, the procedure of senone extraction leads to acoustic correlations among multiple classes corresponding to the same phone-HMM states~\cite{young1994tree}, as they all share the same root in the decision tree (Fig.~\ref{fig:senone-posteriors}(b)).

These dependencies can be characterized by analyzing a large number of senone probabilities from the training data. The frequent dependencies are exhibited as regularities among the correlated dimensions in senone posteriors.
As a result, a matrix formed by concatenation of class-specific senone posteriors has a low-rank structure. In other words, class-specific senones lie in low-dimensional subspaces with a dimension higher than unity~\cite{dighe2016exploiting}, that violates the principal assumption of binary hard targets.

In practice, inaccuracies in DNN training lead to the presence of unstructured high-dimensional errors (Fig.~\ref{fig:senone-posteriors}(c)).
Therefore, the initial senone posterior probabilities obtained from the forward pass of a DNN trained with hard alignments are not accurate in quantifying the senone dependency structures. Our previous work demonstrates that the erroneous estimations can be separated using low-rank or sparse representations~\cite{luyet2016lrr,dighe2016exploiting}. In the present study, we consider application of PCA and sparse coding to obtain more reliable soft targets for DNN acoustic model training.

\begin{figure*}[t]
\centering
\includegraphics[scale=0.33]{theory2}
\vspace{-4mm}
\caption{ \footnotesize Low-dimensional reconstruction of senone posterior probabilities to achieve more accurate soft targets for DNN acoustic model training: PCA is used to extract principle components of the linear subspaces of individual senone classes. Sparse reconstruction over a dictionary of senone space representatives is used for non-linear recovery of low-dimensional structures.}\label{fig:theory}
\vspace{-6mm}
\end{figure*}

\vspace{-3mm}
\subsection{Low-rank Reconstruction Using Eigenposteriors}\label{sec:pca}
\vspace{-2mm}
Let $z_t = [p(s_1|x_t) \hdots p(s_k|x_t) \hdots p(s_K|x_t) ]^\top$ denote a forward pass estimate of the posterior probabilities of $K$ senone classes $\{s_k\}_{k=1}^K$, given the acoustic feature $x_t$ at time $t$. DNN is trained using the initial labels obtained from GMM-HMM forced alignment. We collect $N$ senone posteriors which are labeled as class $s_k$ in GMM-HMM forced alignment and mean-center them in the \textit{logarithmic} domain as follows:
\begin{equation}\label{eq:log_post}
\tilde{z}_t = \ln(z_t) - \mu_{s_k}
\end{equation}
where $\mu_{s_k}$ is mean of the collected posteriors in log-domain. Due to skewed distribution of the posterior vectors, the logarithm of posteriors fits better the Gaussian assumption of PCA. We concatenate the $N$ senone $s_k$ posterior vectors after operation shown in \eqref{eq:log_post} to form a matrix $M_{s_k} \in \mathcal{R}^{K \times N}$. For the sake of brevity, the subscript $s_k$ is dropped in the subsequent expressions. However, all the calculations are performed for each of the senone classes individually.

Principal components of the senone space are obtained via eigenvector decomposition~\cite{shlens2014tutorial} of covariance matrix of $M$.
The covariance matrix is obtained as $C = \frac{1}{N-1}M M^\top$. We factorize the covariance matrix as $C = P S P^\top$ where $P\in\mathcal{R}^{K\times K}$ identifies the eigenvectors and $S$ is a diagonal matrix containing the sorted eigenvalues.
Eigenvectors in $P$ which correspond to the large eigenvalues in $S$ constitute the frequent regularities in the subspace, whereas others carry the high-dimensional unstructured noise.
Hence, the low-rank projection matrix is defined as
\begin{equation}\label{eq:pca}
D_{\text{LR}} = P_l\in \mathcal{R}^{K\times l}
\end{equation}
where $P_l$ is truncation of $P$ that keeps only the first $l$ eigenvectors and discards the erroneous variability captured by other $K-l$ components. We select $l$ such that relatively $\sigma$\% variability is preserved in the low-rank reconstruction of original senone matrix $M$.

The eigenvectors stored in the low-rank projection $P_l$ are referred to as \textit{``eigenposteriors''} of the senone space (in the same spirit as \textit{eigenfaces} are defined for low-dimensional modeling of human faces~\cite{sirovich87faces}).

Low-rank reconstruction of a mean-centered log posterior $\tilde{z}_t$, denoted by $\tilde{z}_t^{\text{LR}}$ is estimated as
\begin{equation}
\tilde{z}_t^{\text{LR}} = D_{\text{LR}} {D_{\text{LR}}}^\top  \tilde{z}_t
\end{equation}

Finally, we add the mean $\mu_{s_k}$ to $\tilde{z}_t^{\text{LR}}$ and take its exponent to obtain a low-rank senone posterior $z^{LR}_t$ for the acoustic frame $x_t$. Low-rank posteriors obtained for the training data are used as soft targets for learning better DNNs (Fig.\ref{fig:theory}).
We assume that $\sigma$\% variability, that quantifies the low-rank regularities in senone spaces, is a parameter independent of the senone class.

\vspace{-3mm}
\subsection{Sparse Reconstruction Using Dictionary Learning}\label{sec:dlsc}
\vspace{-1mm}
Unlike PCA, over-complete dictionary learning and sparse coding enables modeling of non-linear low-dimensional manifolds. Sparse modelling assumes that senone posteriors can be generated as sparse linear combination of senone space representatives, collected in a dictionary $D_{\text{SP}}$.
We use online dictionary learning algorithm~\cite{mairal2010online} to learn an over-complete dictionary for senone $s_k$ using a collection of $N$ training data posteriors of senone $s_k$, such that
\begin{equation}\small \label{eq:dict_learn}
D_{\text{SP}} = \arg \min_{\substack D,A} \sum_{t=t_1}^{t_N} \| z_t - D\,\alpha_{t} \|_2^2 + \lambda{\|\alpha_{t}\|}_
\end{equation}
where $A=[\alpha_{t_1}\hdots\alpha_{t_N}]$ and $\lambda$ is a regularization factor.  Again we have dropped the subscript $s_k$, but all calculations are still senone-specific.
Sparse reconstruction (Fig.\ref{fig:theory}) of senone posteriors is thus obtained by first estimating the sparse representation~\cite{tibshirani1996regression} as
\begin{equation}\small \label{eq:sparse}
\alpha_{t} = \arg \min_{\alpha} \| z_t - D_{\text{SP}}\,\alpha \|_2^2 + \lambda{\|\alpha\|}_1.
\end{equation}
followed by reconstruction as
\begin{equation}\small \label{eq:reconst}
z^{SP}_t = D_{\text{SP}}\; \alpha_{t} \qquad \forall t \in \{t_1,\hdots,t_N\}.
\end{equation}

Sparse reconstructed senone posteriors have been previously found to be more accurate acoustic models for DNN-HMM speech recognition~\cite{dighe2016exploiting}. In particular, it was shown that the rank of senone-specific matrices is much lower after sparse reconstruction. In the present work, we investigate if they could also provide more accurate soft targets for DNN training
Regularization parameter $\lambda$ in~\eqref{eq:dict_learn}-\eqref{eq:sparse} controls the level of sparsity and the level of noise being removed after sparse reconstruction.
Fig.~\ref{fig:theory} summarises the low-rank and sparse reconstruction of senone posteriors.

\vspace{-2.5mm}
\section{Experimental Analysis}\label{sec:analysis}
\vspace{-2mm}
In this section we evaluate the effectiveness of low-rank and sparse soft targets to improve the performance of DNN-HMM speech recognition. We also investigate the importance of better DNN acoustic models to exploit information from untranscribed data.

\begin{table*}[t]\footnotesize
\caption{\footnotesize Performance of various systems (in WER\%) when additional untranscribed training data is used. System 0 is hard-targets based baseline DNN. In paranthesis, SE-0 denotes supervised enhancement of DNN outputs from system 0 and FP-$n$ shows forward pass using system $n$.}
\vspace{-3mm}
\centering
\begin{tabular}{c l c c || c
\hline
System \# &Training Data & PCA($\sigma$=80) & Sparsity($\lambda$=0.1) & Non-Enhanced Soft-Targets\\% & Hard Targets\\
\hline
0 & AMI   (Baseline WER \textbf{32.4\%}) & - & - & -\\% & 32.4\\
1 & AMI(SE-0) & 31.9 & 31.6 & 32.0\\% & -\\
2 & ICSI(FP-1) + AMI(SE-0) & 31.2 & 31.6 & 32.5\\% & -\\
3 & LIB100(FP-1) + AMI(SE-0) & 31.2 & 31.6 & 32.4\\% & \\
4 & LIB100(FP-2) + AMI(SE-0) & 31.0 & 31.8 & 32.4\\% & -\\
5 & LIB100(FP-2) + ICSI(FP-2) + AMI(SE-0) & \textbf{30.9} & 31.7 & 32.4\\% & -\\
\hline
\end{tabular}
\vspace{-4mm}
\label{table:data_augmentation}
\end{table*}

\vspace{-3.5mm}
\subsection{Database and Speech Features}\label{sec:database}
\vspace{-2mm}
Experiments are conducted on AMI corpus~\cite{mccowan2005ami} which contains recordings of spontaneous conversations in meeting scenarios. We use recordings from individual head microphones (IHM) comprising of around 67 hours of \textit{train} set, 9 hours of development, (\textit{dev}) set, and 7 hours \textit{test} set. 10\% of training data is used for cross-validation during DNN training, whereas \textit{dev} set is used for tuning regularization parameters $\sigma$ and $\lambda$. For experiments using untranscribed additional training data, we use ICSI meeting corpus~\cite{janin2003icsi} and Librispeech corpus~\cite{panayotov2015librispeech}. Data from ICSI corpus consists of meeting recordings (around 70 hours). Librispeech data is read speech from audio-books and we use a 100 hour subset of it.

Kaldi toolkit~\cite{povey2011kaldi} is used for training DNN-HMM systems. All DNNs have 9 frames of temporal context at acoustic input and 4 hidden layers with 1200 neurons each. Input features are 39 dimensional MFCC+$\Delta$+$\Delta\Delta$ (39$\times$9=351 dimensional input) and output is 4007 dimensional senone probability vector. AMI pronunciation dictionary has $\sim$23K words and a bigram model for decoding. For dictionary learning and sprase coding, SPAMS toolbox~\cite{mairal2014sparse} is used.

\vspace{-3.5mm}
\subsection{Baseline DNN-HMM using Hard and Soft Targets}\label{sec:results}
\vspace{-2mm}
Our baseline is a hybrid DNN-HMM system trained using forced aligned targets (IHM setup in~\cite{himawan2015learning}). WER using baseline DNN is 32.4\% on AMI \textit{test} set. Another baseline is a DNN trained using non-enhanced soft targets from the baseline. This system gives a WER of 32.0\%. All soft-target based DNNs are randomly initialized and trained using cross-entropy loss backpropagation.

\vspace{-3.5mm}
\subsection{Generation of Low-rank and Sparse Soft Targets}\label{sec:rkt}
\vspace{-2mm}
We group DNN forward pass senone probabilities for the training data into class-specific senone matrices. For this, senone labels from the ground truth based GMM-HMM hard alignments are used. Each matrix is restricted to have $N=10^4$ vectors of $K=4007$ senone probabilities to facilitate computation of principal components and sparse dictionary learning. We found the average rank of senone matrices, defined as the number of singular values required to preserve 95\% variability, to be 44. Dictionaries of size 500 columns were learned for each senone, making them nearly 10 times over-complete. The procedure as depicted in Fig.~\ref{fig:theory} is implemented to generate low-rank and sparse soft-targets.

We also encountered memory issues while storing large matrices of senone probabilities for all training and cross-validation data. It requires enormous amounts of storage space (similar to~\cite{chan2015transferring}). Hence, we preserve precision only upto first two decimal places in soft targets, followed by normalizing the vector to sum 1 before storing on the disk. We assume that essential information might not be in dimensions with very small probabilities. Although such thresholding can be a compromise to our approach, we did some experiments with higher precision (upto 5 decimal places), but there was no significant improvement in ASR. Both low-rank and sparse reconstruction were still computed on full soft-targets without any rounding; we perform thresholding only when storing targets on the disk.

First we tune the variability preserving low-rank reconstruction parameter $\sigma$ and sparsity regularizer $\lambda$ for better ASR performance in AMI \textit{dev} set. When $\sigma$=80\% of variability is preserved in the principal components space, the most accurate soft targets are achieved for DNN acoustic modeling resulting in the smallest WER. Likewise, $\lambda=0.1$ was found the optimal value for sparse reconstruction. It may be noted that in both low-rank and sparse reconstruction, there is an optimal amount of enhancement needed for improving ASR. While less enhancement leads to continued presence of noise in soft targets, too much of it results in loss of essential information.

\vspace{-3.5mm}
\subsection{DNN-HMM Speech Recognition}\label{sec:rkt}
\vspace{-2mm}
Speech recognition using DNNs trained with the new soft targets obtained from low-rank and sparse reconstruction is compared in Table~\ref{table:data_augmentation}). System-0 is the baseline hard target based DNN. System-1 is built by supervised enhancement of soft outputs obtained from system-0 on AMI training data as shown in Fig.~\ref{fig:theory}. As expected, training with the soft targets yields lower WER than the baseline hard targets. We can see that both PCA and sparse reconstruction result in more accurate acoustic modeling, where sparse reconstruction achieves 0.8\% absolute reduction in WER.

Sparse reconstruction is found to work better than low-rank reconstruction for ASR. It can be due to the higher accuracy of sparse model in characterizing the non-linear senone subspaces~\cite{dighe2015sparse}.
Unlike previous works~\cite{dighe2016exploiting,luyet2016lrr} which required two stages of DNN forward pass and explicit low-dimensional projection, a single DNN is learned here that estimates the probabilities directly on a low-dimensional space.

\vspace{-3.5mm}
\subsection{Training with Untranscribed Data}\label{sec:untranscribed}
\vspace{-2mm}
Given an accurate DNN acoustic model and some untranscribed input speech data, we can obtain soft targets for the new data through forward pass.
Assuming that the initial model can generalize well on unseen data, the additional soft targets thus generated can be used to augment our original training data. We propose to learn better DNN acoustic models using this augmented training set. This method is reminiscent of the \textit{knowledge transfer} approach~\cite{hinton2015distilling,chan2015transferring} which is typically used for model compression. In this work, we use the same network architecture for all experiments.

DNNs trained with low-rank and sparse soft targets are used to generate soft targets for ICSI corpus and Librispeech (LIB100) which are sources of untranscribed data. Table~\ref{table:data_augmentation} shows interesting observations from various experiments using data augmentation. First, system-2 is built augmenting enhanced AMI training data with ICSI soft targets generated from system-1. We consider ICSI corpus, consisting of spontaneous speech from meeting recordings, as in-domain with AMI corpus. While PCA based DNN successfully exploits information from this additional ICSI data showing significant improvement from system-1 to system-2, the same is not observed using sparsity based DNN.

Next, system-3 is built by augmenting enhanced AMI data with Librispeech(LIB100) soft targets obtained from system 1. Read audio book speech data from Librispeech is out-of-domain as compared to spontaneous speech in AMI. Still, system-3 achieves similar reductions in WER as observed in system-2 which was built using in-domain ICSI data.

System 4 and 5 were built to further explore if we could extract even more information from the out-of-domain Librispeech data by using soft targets from system-2 instead of system-1. Note that system-2, trained using soft targets from both AMI and ICSI spontaneous speech data, is a more accurate model than system 1. Indeed, both system 4 and 5 perform better than previous systems using PCA based DNNs where system 5 outperforms the hard target based baseline by 1.5\% absolute reduction in WER.

Surprisingly, DNN soft targets obtained from sparse reconstruction are not able to exploit the unseen data in all the systems.
We speculate that dictionary learning for sparse coding captures the non-linearities specific to AMI database. These nonlinear characteristics may correspond to channel and recording conditions which vary over different databases and can not be transcended. On the other hand, the local linearity assumption of PCA leads to extraction of a highly restricted basis set that captures the most important dynamics in the senone probability space. Such regularities mainly address the acoustic dependencies among senones which are generalizable to other acoustic conditions. Hence, the eigenposteriors are invariant to the exceptional effects due to channel and recording conditions.

Sparse reconstruction is able to mitigate the undesired effects as long as they have been seen in the training data. Given the superior performance of sparse reconstruction of AMI posteriors (in system-1), we believe that sparse modeling might be more powerful if some labeled data from unseen acoustic conditions is made available for dictionary learning.

It may be noted that training with additional untranscribed data is not effective if non-enhanced soft targets are used. In fact, systems 2-5 without low-rank or sparse reconstruction, perform worse than system-1 although they have seen more training data.
 \vspace{-2mm}
\section{Conclusions and Future Directions}\label{sec:conclusions}
 \vspace{-2mm}
We presented a novel approach to improve DNN acoustic model training using low-rank and sparse soft targets.
PCA and sparse coding were employed to identify senone subspaces, and enhance senone probabilities through low-dimensional reconstruction. Low-rank reconstruction using PCA relies on the existance of eigenposteriors capturing the local dynamics of senone subspaces.
Although, sparse reconstruction proves more effective to achieve reliable soft targets when transcribed data is provided, low-rank reconstruction is found generalizable to out-of-domain untranscribed data.
DNN trained on low-rank reconstruction acheives 4.6\% relative reduction in WER, whereas DNN trained using non-enhanced soft targets fails to exploit additional information from additional data. Eigenposteriors can be better estimated using robust PCA~\cite{liu2013robust} and sparse PCA~\cite{zou2006sparse} for better modeling of senone subspaces. Furthermore, probabilistic PCA and maximum likelihood eigen decomposition can reduce the computational cost for large scale applications.

This study supports the use of probabilistic outputs for DNN acoustic modeling.
Specifically, enhanced soft targets can be more effective in training small footprint DNNs based on model compression. In future, we plan to investigate their usage in cross-lingual knowledge transfer~\cite{swietojanski2012unsupervised}. We will also study domain adaptation based on the notion of eigenposteriors.

\vspace{-3mm}
\section{Acknowledgments}
\vspace{-2mm}
{ Research leading to these results has received funding from SNSF project on ``Parsimonious Hierarchical Automatic Speech Recognition (PHASER)'' grant agreement number 200021-153507.}

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