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

Yagi, Hideki; Nomura, Ryo

doi:10.1587/transfun.e100.a.1683

Cited by 7 publications

(9 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark 6: As in the first order case, T v (δ, R|X) is equal to R * v (δ, R|X), which denotes the minimum achievable rate of the FV δ-source coding [14]. Theorem 7 also indicates that…”

Section: A Definitionsmentioning

confidence: 96%

See 1 more Smart Citation

Variable-Length Resolvability for Mixed Sources and its Application to Variable-Length Source Coding

Yagi

Han

2018

2018 IEEE International Symposium on Information Theory (ISIT)

Self Cite

View full text Add to dashboard Cite

In the problem of variable-length δ-channel resolvability, the channel output is approximated by encoding a variable-length uniform random number under the constraint that the variational distance between the target and approximated distributions should be within a given constant δ asymptotically. In this paper, we assume that the given channel input is a mixed source whose components may be general sources. To analyze the minimum achievable length rate of the uniform random number, called the δ-resolvability, we introduce a variant problem of the variable-length δ-channel resolvability. A general formula for the δ-resolvability in this variant problem is established for a general channel. When the channel is an identity mapping, it is shown that the δ-resolvability in the original and variant problems coincide. This relation leads to a direct derivation of a single-letter formula for the δ-resolvability when the given source is a mixed memoryless source. We extend the result to the second-order case. As a byproduct, we obtain the first-order and second-order formulas for fixed-to-variable length source coding allowing error probability up to δ.

show abstract

“…Remark 6: As in the first order case, T v (δ, R|X) is equal to R * v (δ, R|X), which denotes the minimum achievable rate of the FV δ-source coding [14]. Theorem 7 also indicates that…”

Section: A Definitionsmentioning

confidence: 96%

“…Let R be v(δ)-achievable for {X i }. Then, there exists U (L (i) n ) and ϕ (i) n satisfying (14) and…”

Section: ) Converse Partmentioning

confidence: 99%

Variable-Length Resolvability for Mixed Sources and its Application to Variable-Length Source Coding

Yagi

Han

2018

2018 IEEE International Symposium on Information Theory (ISIT)

Self Cite

View full text Add to dashboard Cite

show abstract

“…The notion of the optimistic optimum rates has first been introduced by Vembu, Verdú and Steinberg [19] in the source-channel coding framework. Then, several researchers have developed the optimistic coding scenario in other information theoretic problems [10], [20]- [22]. In particular, Hayashi [10] has considered the first-and secondorder optimum intrinsic randomness rates with respect to the variational distance and the KL divergence in the optimistic scenario.…”

Section: A Source Resolvabilitymentioning

confidence: 99%

Source Resolvability and Intrinsic Randomness: Two Random Number Generation Problems With Respect to a Subclass of f-Divergences

Nomura

2020

IEEE Trans. Inform. Theory

Self Cite

View full text Add to dashboard Cite

This paper deals with two typical random number generation problems in information theory. One is the source resolvability problem (resolvability problem for short) and the other is the intrinsic randomness problem. In the literature, optimum achievable rates in these two problems with respect to the variational distance as well as the Kullback-Leibler (KL) divergence have already been analyzed. On the other hand, in this study we consider these two problems with respect to fdivergences. The f-divergence is a general non-negative measure between two probabilistic distributions on the basis of a convex function f. The class of f-divergences includes several important measures such as the variational distance, the KL divergence, the Hellinger distance and so on. Hence, it is meaningful to consider the random number generation problems with respect to f-divergences. In this paper, we impose some conditions on the function f so as to simplify the analysis, that is, we consider a subclass of f-divergences. Then, we first derive general formulas of the first-order optimum achievable rates with respect to f-divergences. Next, we particularize our general formulas to several specified functions f. As a result, we reveal that it is easy to derive optimum achievable rates for several important measures from our general formulas. The second-order optimum achievable rates and optimistic optimum achievable rates have also been investigated.

show abstract

“…In this section, we establish the coding theorems in the optimistic sense, which will turn out to reveal another relationship with the fixed-length source coding. The notion of the optimistic coding has first been introduced by Vembu, Verdú and Steinberg [15] and several researchers have developed the optimistic coding scenario in other information theoretic problems [9], [13], [16]. We also develop the notion of the optimistic coding to the ε-variable-length coding problem.…”

Section: A General Formulasmentioning

confidence: 99%

“…They have revealed that the second-order optimum mean codeword length of the ε-variable-length codes has a completely different behavior with that of the variable-length codes without error [8]. Yagi and Nomura [9] have also characterized the first-and second-order optimum mean codeword cost of the ε-variable-length codes.…”

Section: Introductionmentioning

confidence: 99%

Optimum Overflow Thresholds in Variable-Length Source Coding Allowing Non-Vanishing Error Probability

Nomura

Yagi

2019

IEEE Trans. Inform. Theory

Self Cite

View full text Add to dashboard Cite

The variable-length source coding problem allowing the error probability up to some constant is considered for general sources. In this problem the optimum mean codeword length of variablelength codes has already been determined. On the other hand, in this paper, we focus on the overflow (or excess codeword length) probability instead of the mean codeword length. The infimum of overflow thresholds under the constraint that both of the error probability and the overflow probability are smaller than or equal to some constant is called the optimum overflow threshold.In this paper, we first derive finite-length upper and lower bounds on these probabilities so as to analyze the optimum overflow thresholds. Then, by using these bounds we determine the general formula of the optimum overflow thresholds in both of the first-order and second-order forms. Next, we consider another expression of the derived general formula so as to reveal the relationship with the optimum coding rate in the fixed-length source coding problem. We also derive general formulas of the optimum overflow thresholds in the optimistic coding scenario. Finally, we apply general formulas derived in this paper to the case of stationary memoryless sources.

show abstract

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

Cited by 7 publications

References 15 publications

Variable-Length Resolvability for Mixed Sources and its Application to Variable-Length Source Coding

Variable-Length Resolvability for Mixed Sources and its Application to Variable-Length Source Coding

Source Resolvability and Intrinsic Randomness: Two Random Number Generation Problems With Respect to a Subclass of f-Divergences

Optimum Overflow Thresholds in Variable-Length Source Coding Allowing Non-Vanishing Error Probability

Contact Info

Product

Resources

About