Title: Noise Models in the Nonlinear Spectral Domain for Optical Fibre Communications,
Abstract: Existing works on building a soliton transmission system only encode
information using the imaginary part of the eigenvalue, which fails to make
full use of the signal degree-of-freedoms. Motivated by this observation, we
make the first step of encoding information using (discrete) spectral
amplitudes by proposing analytical noise models for the spectral amplitudes of
$N$-solitons ($N\geq 1$). To our best knowledge, this is the first work in
building an analytical noise model for spectral amplitudes, which leads to many
interesting information theoretic questions, such as channel capacity analysis,
and has a potential of increasing the transmission rate. The noise statistics
of the spectral amplitude of a soliton are also obtained without the Gaussian
approximation.