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

Kuzuoka, Shigeaki; Watanabe, Shun

doi:10.1109/tit.2015.2424406

“…So far, the study of distributed computing has been restricted to the fixed-length coding in the literature [4], [5]. In this paper, by using the techniques developed by the authors in [10], we show that the above mentioned results also hold even for the variable-length coding.…”

Section: Symbol-wise Functionssupporting

confidence: 53%

“…10 In other words, the first nρ symbols of f n (x, y) is symbol-wise addition in GF(p) and the remaining part of f n (x, y) is identical with the last n(1−ρ) symbols of (x, y). We can see that f = {f n } ∞ n=1…”

Section: G Proof Of Theoremmentioning

confidence: 99%

A Dichotomy of Functions in Distributed Coding: An Information Spectral Approach

Kuzuoka

¹

,

Watanabe

²

2015

IEEE Trans. Inform. Theory

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The problem of distributed data compression for function computation is considered, where (i) the function to be computed is not necessarily symbol-wise function and (ii) the information source has memory and may not be stationary nor ergodic. We introduce the class of smooth sources and give a sufficient condition on functions so that the achievable rate region for computing coincides with the Slepian-Wolf region (i.e., the rate region for reproducing the entire source) for any smooth sources. Moreover, for symbol-wise functions, the necessary and sufficient condition for the coincidence is established. Our result for the full side-information case is a generalization of the result by Ahlswede and Csiszár to sources with memory; our dichotomy theorem is different from Han and Kobayashi's dichotomy theorem, which reveals an effect of memory in distributed function computation. All results are given not only for fixed-length coding but also for variable-length coding in a unified manner. Furthermore, for the full side-information case, the error probability in the moderate deviation regime is also investigated.

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“…We shall prove (i) (1 − δ)H(X) ≤ lim γ↓0 H * (i) Proof of (1 − δ)H(X) ≤ lim γ↓0 H * [δ+γ] (X): This inequality can be proven similarly to [8,Theorem 4] and [10,Theorem 3], which show (1 − δ)H(X) ≤ lim γ↓0 H [δ+γ] (X). We describe the whole proof for readers' convenience.…”

Section: Appendix a Proofs Of Equations (14) And (15)mentioning

confidence: 88%

“…It is of use to notice relations among H [δ] (X), H * [δ] (X) and information spectrum quantities [2]. Following arguments on H [δ+γ] (X) in [8], [10], we obtain 1…”

Section: Variable-length Coding With Costmentioning

confidence: 97%

See 1 more Smart Citation

Variable-Length Coding with Cost Allowing Non-Vanishing Error Probability

Yagi

¹

,

Nomura

²

2017

IEICE Trans. Fundamentals

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Abstract-We derive a general formula of the minimum achievable rate for fixed-to-variable length coding with a regular cost function by allowing the error probability up to a constant ε. For a fixed-to-variable length code, we call the set of source sequences that can be decoded without error the dominant set of source sequences. For any two regular cost functions, it is revealed that the dominant set of source sequences for a code attaining the minimum achievable rate with a cost function is also the dominant set for a code attaining the minimum achievable rate with the other cost function. We also give a general formula of the second-order minimum achievable rate.

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A dichotomy of functions in distributed coding: An information spectral approach

Kuzuoka

¹

,

Watanabe

²

2015

2015 IEEE International Symposium on Information Theory (ISIT)

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The problem of distributed data compression for function computation is considered, where (i) the function to be computed is not necessarily symbol-wise function and (ii) the information source has memory and may not be stationary nor ergodic. We introduce the class of smooth sources and give a sufficient condition on functions so that the achievable rate region for computing coincides with the Slepian-Wolf region (i.e., the rate region for reproducing the entire source) for any smooth sources. Moreover, for symbol-wise functions, the necessary and sufficient condition for the coincidence is established. Our result for the full side-information case is a generalization of the result by Ahlswede and Csiszár to sources with memory; our dichotomy theorem is different from Han and Kobayashi's dichotomy theorem, which reveals an effect of memory in distributed function computation. All results are given not only for fixed-length coding but also for variable-length coding in a unified manner. Furthermore, for the full side-information case, the error probability in the moderate deviation regime is also investigated. Index Termsdistributed computing, information-spectrum method, Slepian-Wolf coding I. INTRODUCTIONWe study the problem of distributed data compression for function computation described in Fig. 1 and Fig. 2, where the function to be computed is not necessarily symbol-wise function. In [1], Körner and Marton revealed that the achievable rate region for computing modulo-sum is strictly larger than the rate region that can be achieved by first applying Slepian-Wolf coding [2] and then computing the function. 1 Since then, distributed coding schemes that are tailored for some classes of functions were studied (e.g., see [3, Chapter 21]). These results are the cases such that the structure of functions can be utilized for distributed coding. However, not all functions have such nice structures, and even for some classes of functions, it is known that the Slepian-Wolf region cannot be improved at

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

Cited by 10 publications

References 35 publications

A Dichotomy of Functions in Distributed Coding: An Information Spectral Approach

A Dichotomy of Functions in Distributed Coding: An Information Spectral Approach

Variable-Length Coding with Cost Allowing Non-Vanishing Error Probability

A dichotomy of functions in distributed coding: An information spectral approach

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