We study the distributed simulation problem where @math players aim to generate sequences of random coin flips where some subsets of the players share an independent common coin which can be tossed multiple times, and there is a publicly seen blackboard through which the players communicate with each other. We provide a tight representation of the optimal communication rates via linear programming, and more importantly, propose explicit algorithms for the optimal distributed simulation for a wide class of hypergraphs. In particular, the optimal communication rate in complete hypergraphs is still achievable in sparser hypergraphs containing a path-connected cycle-free cluster of topologically connected components. Some key steps in analyzing the upper bounds rely on two different definitions of connectivity in hypergraphs, which may be of independent interest.
@cite_36: We derive single-letter characterizations of (strong) secrecy capacities for models with an arbitrary number of terminals, each of which observes a distinct component of a discrete memoryless multiple source, with unrestricted and interactive public communication permitted between the terminals. A subset of these terminals can serve as helpers for the remaining terminals in generating secrecy. According to the extent of an eavesdropper's knowledge, three kinds of secrecy capacity are considered: secret key (SK), private key (PK), and wiretap secret key (WSK) capacity. The characterizations of the SK and PK capacities highlight the innate connections between secrecy generation and multiterminal source coding without secrecy requirements. A general upper bound for WSK capacity is derived which is tight in the case when the eavesdropper can wiretap noisy versions of the components of the underlying multiple source, provided randomization is permitted at the terminals. These secrecy capacities are seen to be achievable with noninteractive communication between the terminals. The achievability results are also shown to be universal.
@cite_21: The author determines for arbitrarily varying channels a) the average error capacity and b) the maximal error capacity in case of randomized encoding.
@cite_0: The bottleneck of the state-of-the-art algorithms for geometric Steiner problems is usually the concatenation phase, where the prevailing approach treats the generated full Steiner trees as edges of a hypergraph and uses an LP-relaxation of the minimum spanning tree in hypergraph (MSTH) problem. We study this original and some new equivalent relaxations of this problem and clarify their relations to all classical relaxations of the Steiner problem. In an experimental study, an algorithm of ours which is designed for general graphs turns out to be an efficient alternative to the MSTH approach.
@cite_27: A well-known result of R. Ahlswede (1970) asserts that the deterministic code capacity of an arbitrarily varying channel (AVC), under the average-error-probability criterion, either equals its random code capacity or else is zero. A necessary and sufficient condition is identified for deciding between these alternative, namely, the capacity is zero if and only if the AVC is symmetrizable. The capacity of the AVC is determined with constraints on the transmitted codewords as well as on the channel state sequences, and it is demonstrated that it may be positive but less than the corresponding random code capacity. A special case of the results resolves a weakened version of a fundamental problem of coding theory. >
@cite_34: We study the generation of a secret key of maximum rate by a pair of terminals observing correlated sources and with the means to communicate over a noiseless public communication channel. Our main result establishes a structural equivalence between the generation of a maximum rate secret key and the generation of a common randomness that renders the observations of the two terminals conditionally independent. The minimum rate of such common randomness, termed interactive common information, is related to Wyner's notion of common information, and serves to characterize the minimum rate of interactive public communication required to generate an optimum rate secret key. This characterization yields a single-letter expression for the aforementioned communication rate when the number of rounds of interaction are bounded. An application of our results shows that interaction does not reduce this rate for binary symmetric sources. Further, we provide an example for which interaction does reduce the minimum rate of communication. Also, certain invariance properties of common information quantities are established that may be of independent interest.
@cite_13: The problem of generating a shared secret key S by two parties knowing dependent random variables X and Y, respectively, but not sharing a secret key initially, is considered. An enemy who knows the random variable Z, jointly distributed with X and Y according to some probability distribution P sub XYZ , can also receive all messages exchanged by the two parties over a public channel. The goal of a protocol is that the enemy obtains at most a negligible amount of information about S. Upper bounds on H(S) as a function of P sub XYZ are presented. Lower bounds on the rate H(S) N (as N to infinity ) are derived for the case in which X=(X sub 1 , . . ., X sub N ), Y=(Y sub 1 , . . ., Y sub N ) and Z=(Z sub 1 , . . ., Z sub N ) result from N independent executions of a random experiment generating X sub i , Y sub i and Z sub i for i=1, . . ., N. It is shown that such a secret key agreement is possible for a scenario in which all three parties receive the output of a binary symmetric source over independent binary symmetric channels, even when the enemy's channel is superior to the other two channels. >
@cite_17: The problem of finding a meaningful measure of the "common information" or "common randomness' of two discrete dependent random variables X,Y is studied. The quantity C(X; Y) is defined as the minimum possible value of I(X, Y; W) where the minimum is taken over all distributions defining an auxiliary random variable W W , a finite set, such that X, Y are conditionally independent given W . The main result of the paper is contained in two theorems which show that C(X; Y) is i) the minimum R_0 such that a sequence of independent copies of (X,Y) can be efficiently encoded into three binary streams W_0, W_1,W_2 with rates R_0,R_1,R_2 , respectively, [ R_i = H(X, Y)] and X recovered from (W_0, W_1) , and Y recovered from (W_0, W_2) , i.e., W_0 is the common stream; ii) the minimum binary rate R of the common input to independent processors that generate an approximation to X,Y .
The role of public randomness has been given considerable attention in information theory literature starting from Wyner @cite_17 who characterized the minimum rate of public randomness required for two processors to produce (approximatley) independent copies of random variables @math . Public randomness was used for encoding and decoding in arbitrary varying channels by Ahlswede @cite_21 , and Csisz 'ar and Narayan @cite_27 . Generation of public randomness between two users which should be hidden from an eavesdropper was studied in secret key agreement by Maurer @cite_13 , and Ahlswede and Csisz 'ar @cite_0 . Secret key agreement between multiple users was studied by Csisz 'ar and Narayan @cite_36 , and the minimum communication rate required to generate secret key between two users was studied by Tyagi @cite_34 .