Zero error coordination

Abroshan, Mahed; Gohari, Amin; Jaggi, Sidharth

doi:10.1109/itwf.2015.7360763

Cited by 6 publications

(5 citation statements)

References 27 publications

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“…The results for empirical coordination are extended to general alphabets in [35] and [36], by considering standard Borel spaces. The problems of zero-error coordination [37] and of strong coordination with an evaluation function [38] are both related to graph theory.…”

Section: Introductionmentioning

confidence: 99%

Joint Empirical Coordination of Source and Channel

Treust

2017

IEEE Trans. Inform. Theory

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International audienceIn a decentralized and self-configuring network, the communication devices are considered as autonomous decision-makers that sense their environment and that implement optimal transmission schemes. It is essential that these autonomous devices cooperate and coordinate their actions, to ensure the reliability of the transmissions and the stability of the network. We study a point-to-point scenario in which the encoder and the decoder implement decentralized policies that are coordinated. The coordination is measured in terms of empirical frequency of symbols of source and channel. The encoder and the decoder perform a coding scheme such that the empirical distribution of the symbols is close to a target joint probability distribution. We characterize the set of achievable target probability distributions for a point-to-point source-channel model, in which the encoder is non-causal and the decoder is strictly causal i.e., it returns an action based on the observation of the past channel outputs. The objectives of the encoder and of the decoder, are captured by some utility function, evaluated with respect to the set of achievable target probability distributions. In this article, we investigate the maximization problem of a utility function that is common to both encoder and decoder. We show that the compression and the transmission of information are particular cases of the empirical coordination

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Section: Introductionmentioning

confidence: 99%

Joint Empirical Coordination of Source and Channel

Treust

2017

IEEE Trans. Inform. Theory

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“…To the best of our knowledge, we define the notion of channel diameter Diam α (p(y|x)) for the first time. Theorem 10 implies that the exact simulation of p(y|x) with a noiseless link of rate R with infinite shared randomness is possible only if C ∞ (p(y|x)) ≤ R. In fact, as shown in [8] (see [6] for a discussion), C ∞ (p(y|x)) ≤ R is a sufficient and necessary condition for exact simulation of p(y|x) with a noiseless link of rate R.…”

Section: Broadcast Channel Simulationmentioning

confidence: 96%

“…Fortunately, the reverse problem has a clean solution when infinite shared randomness is available, given in [8]. While the authors in [8] do not explicitly express their solution in terms of the Rényi mutual information, one can observe that their answer is the Rényi capacity of order infinity of the channel (see [6] for a discussion).…”

Section: Introductionmentioning

confidence: 99%

“…Thus, any of the models can be conceived when limited share randomness exists between the transmitter and the receiver. We would like to emphasize that one can also conceive other notions of channel simulation, which we do not consider in this work, e.g., average distortion ( d-distance) measure as in [18,19,20], agreement probability as in [22], the empirical coordination of [23] or the exact simulation of [5]; see also [6,7].…”

Section: Introductionmentioning

confidence: 99%

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Simulation of a Channel with Another Channel

Haddadpour

Yassaee

Beigi

et al. 2016

IEEE Trans. Inform. Theory

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In this paper, we study the problem of simulating a discrete memoryless channel (DMC) from another DMC under an average-case and an exact model. We present several achievability and infeasibility results, with tight characterizations in special cases. In particular for the exact model, we fully characterize when a binary symmetric channel (BSC) can be simulated from a binary erasure channel (BEC) when there is no shared randomness. We also provide infeasibility and achievability results for simulation of a binary channel from another binary channel in the case of no shared randomness. To do this, we use properties of Rényi capacity of a given order. We also introduce a notion of "channel diameter" which is shown to be additive and satisfy a data processing inequality.

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“…Cover et al [7] characterized the empirical coordination needed for some 3-node problems. Abroshan et al [8] considered an exact, zero error coordination instead of an asymptotically vanishing error and employed the notion of set coordination, which bears similarities with the empirical notion of coordination. The problem of channel simulation became a subject of interest in recent years.…”

Section: Related Workmentioning

confidence: 99%

Some Results on Distributed Source Simulation with no Communication

Berg

Shayevitz

Kim

et al. 2019

2019 IEEE Information Theory Workshop (ITW)

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We consider the problem of distributed source simulation with no communication, in which Alice and Bob observe sequences U n and V n respectively, drawn from a joint distribution p ⊗n U V , and wish to locally generate sequences X n and Y n respectively with a joint distribution that is close (in KL divergence) to p ⊗n XY . We provide a single-letter condition under which such a simulation is asymptotically possible with a vanishing KL divergence. Our condition is nontrivial only in the case where the Gàcs-Körner (GK) common information between U and V is nonzero, and we conjecture that only scalar Markov chains X − U − V − Y can be simulated otherwise. Motivated by this conjecture, we further examine the case where both pUV and pXY are doubly symmetric binary sources with parameters p, q ≤ 1/2 respectively. While it is trivial that in this case p ≤ q is both necessary and sufficient, we show that when p is close to q then any successful simulation is close to being scalar in the total variation sense. Figure 2: Digital solutionThis digital approach is viable only when C GK (U ; V ) > 0. There is an even simpler analog approach that does not use common information -Alice and Bob pass their corresponding sequences through memoryless channels p X n |U n = p ⊗n X|U and p Y n |V n = p ⊗n Y |V , respectively, symbol-by-symbol.Proposition 2 (analog solution). If X − U − V − Y form a Markov chain, then p XY is simulable from p UV .

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Zero error coordination

Cited by 6 publications

References 27 publications

Joint Empirical Coordination of Source and Channel

Joint Empirical Coordination of Source and Channel

Simulation of a Channel with Another Channel

Some Results on Distributed Source Simulation with no Communication

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