Distributed Source Simulation With No Communication

Berg, Tomer; Shayevitz, Ofer; Kim, Young-Han; Wang, Lele

doi:10.48550/arxiv.1906.06970

2019

DOI: 10.48550/arxiv.1906.06970

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Distributed Source Simulation With No Communication

Tomer Berg

Ofer Shayevitz

Young-Han Kim

et al.

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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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Some Results on Distributed Source Simulation with no Communication

Berg

Shayevitz

Kim

et al. 2019

2019 IEEE Information Theory Workshop (ITW)

Self Cite

View full text Add to dashboard Cite

show abstract

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Distributed Source Simulation With No Communication

Cited by 1 publication

References 32 publications

Some Results on Distributed Source Simulation with no Communication

Some Results on Distributed Source Simulation with no Communication

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