Nonasymptotic and Second-Order Achievability Bounds for Coding With Side-Information

Self Cite

This paper studies variable-length (VL) source coding of general sources with side-information. Novel one-shot coding bounds for Slepian-Wolf (SW) coding, which give nonasymptotic tradeoff between the error probability and the codeword length of VL-SW coding, are established. One-shot results are applied to asymptotic analysis, and a general formula for the optimal coding rate achievable by weakly lossless VL-SW coding (i.e., VL-SW coding with vanishing error probability) is derived. Our general formula reveals how the encoder side-information and/or VL coding improve the optimal coding rate in the general setting. In addition, it is shown that if the encoder side-information is useless in weakly lossless VL coding then it is also useless even in the case where the error probability may be positive asymptotically.Index Terms-ε source coding, information-spectrum method, multiterminal source coding, one-shot coding theorem, side-information, Slepian-Wolf coding, weak variable-length coding.

Section: A Case Where Encoder Side-information Is Uselessmentioning

confidence: 97%

An Information-Spectrum Approach to Weak Variable-Length Source Coding With Side-Information

Kuzuoka

Watanabe

2015

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“…[60]). In place of the covering lemma, we can also use a reverse Shannon theorem to simulate a test channel, which simplifies proofs and sometimes provide tighter bounds; see, for instance, [176], [120], [174], [170], [155], [100].…”

Section: A the Reverse Shannon Theoremmentioning

confidence: 99%

Communication for Generating Correlation: A Unifying Survey

Sudan

Tyagi

Watanabe

2020

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The task of manipulating correlated random variables in a distributed setting has received attention in the fields of both Information Theory and Computer Science. Often shared correlations can be converted, using a little amount of communication, into perfectly shared uniform random variables. Such perfect shared randomness, in turn, enables the solutions of many tasks. Even the reverse conversion of perfectly shared uniform randomness into variables with a desired form of correlation turns out to be insightful and technically useful. In this article, we describe progress-to-date on such problems and lay out pertinent measures, achievability results, limits of performance, and point to new directions.M. Sudan is with the 13 When X1, Z, and X2 form Markov chain in this order, the SK capacity is 0. 14 The benefit of feedback in the context of the wiretap channel was pointed out in [119].

“…Hence, we can upper boundC ρ =C ρ (G|X, Y ) as follows. 8 (191) 8 The following step is essentially same as that of Proposition 4 of Arikan [2]. and thus, for each i,…”

Section: B Proof Of Theoremmentioning

confidence: 99%

“…By general formula, we mean that we consider sequences of guessing problems and do not place any underlying structure such as stationarity, memorylessness and ergodicity on the source[7],[8].January 25, 2019 DRAFT…”

mentioning

confidence: 99%

On the Conditional Smooth Rényi Entropy and its Applications in Guessing and Source Coding

Kuzuoka

2020

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A novel definition of the conditional smooth Rényi entropy, which is different from that of Renner and Wolf, is introduced. It is shown that our definition of the conditional smooth Rényi entropy is appropriate to give lower and upper bounds on the optimal guessing moment in a guessing problem where the guesser is allowed to stop guessing and declare an error. Further a general formula for the optimal guessing exponent is given. In particular, a single-letterized formula for mixture of i.i.d. sources is obtained. Another application in the problem of source coding with the common side-information available at the encoder and decoder is also demonstrated. Index Termsguessing, information-spectrum method, side information, source coding, the conditional smooth Rényi entropy