Moderate-deviations of lossy source coding for discrete and Gaussian sources

Tan, Vincent Y. F.

doi:10.1109/isit.2012.6284697

Cited by 34 publications

(40 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Dembo and Zeitouni [13, Theorem 3.7.1]). We remark that the moderate deviations result for DMSes in Tan [37] for the point-to-point lossy source coding problem requires that nρ 2 n log n → ∞ as n → ∞. However, our proof only requires the condition that nρ 2 n → ∞ as n → ∞.…”

Section: Theorem 5 Under Conditions (I) To (Iv) Depending On the Vamentioning

confidence: 78%

“…The achievability part can be done in a similar manner as [37,Theorem 5]. Here we provide an alternative proof which parallels our analysis for a DMS in Section V-A and the achievability proof of second-order asymptotics for the a GMS in Section VI-B.…”

Section: Proof Of Moderate Deviations (Theorem 15)mentioning

confidence: 80%

“…This is expected since the dispersion of lossy source coding for Gaussian sources is 1/2 nats 2 per source symbol [27], [28]. Similarly the moderate deviations constant for Gaussian rate-distortion also does not depend on the distortion level and the source variance [37].…”

Section: Theorem 15mentioning

confidence: 83%

See 2 more Smart Citations

Second-Order and Moderate Deviation Asymptotics for Successive Refinement

Zhou

Tan

Motani

2017

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

We derive the optimal second-order coding region and moderate deviations constant for successive refinement source coding with a joint excess-distortion probability constraint. We consider two scenarios: (i) a discrete memoryless source (DMS) and arbitrary distortion measures at the decoders and (ii) a Gaussian memoryless source (GMS) and quadratic distortion measures at the decoders. For a DMS with arbitrary distortion measures, we prove an achievable second-order coding region, using type covering lemmas by Kanlis and Narayan and by No, Ingber and Weissman. We prove the converse using the perturbation approach by Gu and Effros. When the DMS is successively refinable, the expressions for the second-order coding region and the moderate deviations constant are simplified and easily computable. For this case, we also obtain new insights on the second-order behavior compared to the scenario where separate excess-distortion proabilities are considered. For example, we describe a DMS, for which the optimal second-order region transitions from being characterizable by a bivariate Gaussian to a univariate Gaussian, as the distortion levels are varied. We then consider a GMS with quadratic distortion measures. To prove the direct part, we make use of the sphere covering theorem by Verger-Gaugry, together with appropriately-defined Gaussian type classes. To prove the converse, we generalize Kostina and Verdú's one-shot converse bound for point-to-point lossy source coding. We remark that this proof is applicable to general successively refinable sources. In the proofs of the moderate deviations results for both scenarios, we follow a strategy similar to that for the second-order asymptotics and use the moderate deviations principle.

show abstract

Section: Theorem 5 Under Conditions (I) To (Iv) Depending On the Vamentioning

confidence: 78%

Section: Proof Of Moderate Deviations (Theorem 15)mentioning

confidence: 80%

See 1 more Smart Citation

Second-Order and Moderate Deviation Asymptotics for Successive Refinement

Zhou

Tan

Motani

2017

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

show abstract

“…So far, three kinds of asymptotic regimes have been studied in the information theory [1], [2], [17], [18], [19], [20], [21]:…”

Section: A Motivationmentioning

confidence: 99%

Non-asymptotic and asymptotic analyses on Markov chains in several problems

Hayashi

Watanabe

2014

2014 Information Theory and Applications Workshop (ITA)

View full text Add to dashboard Cite

Abstract-In this paper, we derive non-asymptotic achievability and converse bounds on the source coding with side-information and the random number generation with side-information. Our bounds are efficiently computable in the sense that the computational complexity does not depend on the block length. We also characterize the asymptotic behaviors of the large deviation regime and the moderate deviation regime by using our bounds, which implies that our bounds are asymptotically tight in those regimes. We also show the second order rates of those problems, and derive single letter forms of the variances characterizing the second order rates.

show abstract

“…B2-1) The large deviation regime in which the error probability ε asymptotically behaves like e −nr for some r > 0 [14], B2-2) The moderate deviation regime in which ε asymptotically behaves like e −n 1−2t r for some r > 0 and t ∈ (0, 1/2) [15], [16], [17], and B2-3) The second order regime in which ε is a constant [18], [4], [5], [6], [15], [16], [19]. We shall claim that a good non-asymptotic bound should be asymptotically optimal in at least one of the above mentioned three regimes.…”

Section: A Uniform Random Number Generation (Urng)mentioning

confidence: 99%

Uniform Random Number Generation From Markov Chains: Non-Asymptotic and Asymptotic Analyses

Hayashi

Watanabe

2016

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

Abstract-In this paper, we derive non-asymptotic achievability and converse bounds on the random number generation with/without side-information. Our bounds are efficiently computable in the sense that the computational complexity does not depend on the block length. We also characterize the asymptotic behaviors of the large deviation regime and the moderate deviation regime by using our bounds, which implies that our bounds are asymptotically tight in those regimes. We also show the second order rates of those problems, and derive single letter forms of the variances characterizing the second order rates. Further, we address the relative entropy rate and the modified mutual information rate for these problems.

show abstract

Moderate-deviations of lossy source coding for discrete and Gaussian sources

Cited by 34 publications

References 22 publications

Second-Order and Moderate Deviation Asymptotics for Successive Refinement

Second-Order and Moderate Deviation Asymptotics for Successive Refinement

Non-asymptotic and asymptotic analyses on Markov chains in several problems

Uniform Random Number Generation From Markov Chains: Non-Asymptotic and Asymptotic Analyses

Contact Info

Product

Resources

About