A comment on "A rate of convergence result for a universal D-semifaithful code"

Merhav, Neri

doi:10.1109/18.391272

Cited by 16 publications

(7 citation statements)

References 2 publications

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“…It would be interesting to study the rate of this convergence. The techniques for computing the redundancy of rate distortion codes [27], [23], [43] should be extendable to Wyner-Ziv codes, leading to an upper bound , since the redundancy of a Wyner-Ziv block code of length upper-bounds the difference . Proving a lower bound of matching order may be more challenging.…”

Section: Discussionmentioning

confidence: 99%

Source Coding With Limited-Look-Ahead Side Information at the Decoder

Weissman

Gamal

2006

IEEE Trans. Inform. Theory

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Abstract-We characterize the rate distortion function for the source coding with decoder side information setting when the ith reconstruction symbol is allowed to depend only on the first i +s ide information symbols, for some finite look-ahead`, in addition to the index from the encoder. For the case of causal side information, i.e.,`= 0, we find that the penalty of causality is the omission of the subtracted mutual information term in the Wyner-Ziv rate distortion function. For`> 0, we derive a computable "infinite-letter" expression for the rate distortion function. When specialized to the near-lossless case, our results characterize the best achievable rate for the Slepian-Wolf source coding problem with finite side information looka-head, and have some surprising implications. We find that side information is useless for any fixedẁ hen the joint probability mass function (PMF) of the source and side information satisfies the positivity condition P (x; y) > 0 for all (x; y). More generally, the optimal rate depends on the distribution of the pair X; Y only through the distribution of X and the bipartite graph whose edges represent the pairs x; y for which P (x; y) > 0. On the other hand, if side information look-ahead is allowed to grow faster than logarithmic in the block length, then H (X j Y ) is achievable. Finally, we apply our approach to derive a computable expression for channel capacity when state information is available at the encoder with limited look-ahead.

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Section: Discussionmentioning

confidence: 99%

Source Coding With Limited-Look-Ahead Side Information at the Decoder

Weissman

Gamal

2006

IEEE Trans. Inform. Theory

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“…They showed that the average rate of this D-semifaithful code achieves (uniformly over this family) the rate-distortion function at a rate of convergence that is O(n −1 log n). On the optimality of this last constructive result, it is showed in [23] that the rate O(n −1 log n) is optimal at least for the Hamming distortion measure. This optimality was showed more generally in [24] and they also presented new schemes that achieve the optimal rate of convergence of O(n −1 (log n + o(log n)))…”

Section: B Related Work On Universal D-semifaithful For Finite Alphab...mentioning

confidence: 98%

Universal D-Semifaithfull Coding for Countably Infinite Alphabets

Silva

Piantanida

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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The problem of variable length and fixed-distortion universal source coding (or D-semifaithful source coding) for stationary and memoryless sources on countably infinite alphabets (∞-alphabets) is addressed in this paper. The main results of this work offer a set of sufficient conditions (from weaker to stronger) to obtain weak minimax universality, strong minimax universality, and corresponding achievable rates of convergences for the worse-case redundancy for the family of stationary memoryless sources whose densities are dominated by an envelope function (or the envelope family) on ∞-alphabets. An important implication of these results is that universal D-semifaithful source coding is not feasible for the complete family of stationary and memoryless sources on ∞-alphabets. To demonstrate this infeasibility, a sufficient condition for the impossibility is presented for the envelope family. Interestingly, it matches the wellknown impossibility condition in the context of lossless (variable-length) universal source coding. More generally, this work offers a simple description of what is needed to achieve universal D-semifaithful coding for a family of distributions Λ. This reduces to finding a collection of quantizations of the product space at different block-lengths -reflecting the fixed distortion restriction -that satisfy two asymptotic requirements: the first is a universal quantization condition with respect to Λ, and the second is a vanishing information radius (I-radius) condition for Λ reminiscent of the condition known for lossless universal source coding.

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“…Recently, several papers have been devoted to the redundancy problem in rate-distortion theory, such as Yu and Speed [82], Linder, Lugosi, and Zeger [61], Merhav [65], Zhang, Yang, and Wei [83]. One version of the problem concerns the "rate redundancy" of -semifaithful codes.…”

Section: A Rate-distortion Theorymentioning

confidence: 99%

The method of types [information theory]

Csiszár

1998

IEEE Trans. Inform. Theory

328

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The method of types is one of the key technical tools in Shannon Theory, and this tool is valuable also in other fields. In this paper, some key applications will be presented in sufficient detail enabling an interested nonspecialist to gain a working knowledge of the method, and a wide selection of further applications will be surveyed. These range from hypothesis testing and large deviations theory through error exponents for discrete memoryless channels and capacity of arbitrarily varying channels to multiuser problems. While the method of types is suitable primarily for discrete memoryless models, its extensions to certain models with memory will also be discussed.Index Terms-Arbitrarily varying channels, choice of decoder, counting approach, error exponents, extended type concepts, hypothesis testing, large deviations, multiuser problems, universal coding.

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A comment on "A rate of convergence result for a universal D-semifaithful code"

Cited by 16 publications

References 2 publications

Source Coding With Limited-Look-Ahead Side Information at the Decoder

Source Coding With Limited-Look-Ahead Side Information at the Decoder

Universal D-Semifaithfull Coding for Countably Infinite Alphabets

The method of types [information theory]

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