Kaspi Problem Revisited: Non-Asymptotic Converse Bound and Second-Order Asymptotics

Zhou, Lin; Motani, Mehul

doi:10.1109/glocom.2017.8254168

Cited by 5 publications

(4 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the rate-distortion problem that deals with point-to-point lossy data compression, the second-order asymptotics for a DMS were derived by Ingber and Kochman [11], and both finite blocklength bounds and secondorder asymptotics were derived by Kostina and Verdú [12] for a DMS and a Gaussian memoryless source (GMS). The results in [11,12] were further generalized to various scenarios in the point-to-point case [13,14,15,16,17,18] and to problems in network information theory [19,20,21,22,23,24], usually for a DMS.…”

Section: Motivationmentioning

confidence: 99%

“…Specifically, [7,Chapter 3] focuses on the point-to-point setting by presenting non-asymptotic and refined asymptotics bounds for both lossless and lossy source coding problems, [7,Chapter 4.5] briefly presents the results for joint source-channel coding without proof sketches while [7,Chapter 6] studies a lossless multiterminal source coding problem named the Slepian-Wolf problem [30]. It is important to note that recent advances of lossy source coding (e.g., [13,18,16,24]) and the multiterminal cases [19,20,21,22,23,24] are not included in [7]. Our monograph aims to fill the missing piece of finite blocklength analyses by summarizing recent theoretical advances for finite blocklength lossy source coding problems.…”

Section: Motivationmentioning

confidence: 99%

“…Kaspi's asymptotic results were recently refined by Zhou and Motani in [20,19], in which the authors derived non-asymptotic and second-order asymptotics bounds for the Kaspi problem. In this chapter, we present the results in [20,19] and illustrate the role of side information on lossy data compression in the finite blocklength regime. Specifically, we first present a parametric representation for the Kaspi rate-distortion function.…”

Section: Kaspi Problemmentioning

confidence: 99%

See 2 more Smart Citations

On Finite Blocklength Lossy Source Coding

Zhang¹,

Motani²

2023

Preprint

View full text Add to dashboard Cite

Section: Motivationmentioning

confidence: 99%

Section: Motivationmentioning

confidence: 99%

Section: Kaspi Problemmentioning

confidence: 99%

See 1 more Smart Citation

On Finite Blocklength Lossy Source Coding

Zhang¹,

Motani²

2023

Preprint

View full text Add to dashboard Cite

“…The setting of the Kaspi problem is shown in Figure 1 where we have one encoder f and two decoders φ 1 , φ 2 . The side information Y n is available to the encoder f and the decoder φ 2 but not to the decoder φ 1 . The encoder f compresses the source X n into a message S given the side information Y n .…”

Section: Introductionmentioning

confidence: 99%

Non-Asymptotic Converse Bounds and Refined Asymptotics for Two Source Coding Problems

Zhou

Motani

2019

IEEE Trans. Inform. Theory

Self Cite

View full text Add to dashboard Cite

In this paper, we revisit two multi-terminal lossy source coding problems: the lossy source coding problem with side information available at the encoder and one of the two decoders, which we term as the Kaspi problem (Kaspi, 1994), and the multiple description coding problem with one semi-deterministic distortion measure, which we refer to as the Fu-Yeung problem (Fu and Yeung, 2002). For the Kaspi problem, we first present the properties of optimal test channels. Subsequently, we generalize the notion of the distortion-tilted information density for the lossy source coding problem to the Kaspi problem and prove a nonasymptotic converse bound using the properties of optimal test channels and the well-defined distortion-tilted information density. Finally, for discrete memoryless sources, we derive refined asymptotics which includes the second-order, large and moderate deviations asymptotics. In the converse proof of second-order asymptotics, we apply the Berry-Esseen theorem to the derived non-asymptotic converse bound. The achievability proof follows by first proving a type-covering lemma tailored to the Kaspi problem, then properly Taylor expanding the well-defined distortion-tilted information densities and finally applying the Berry-Esseen theorem. We then generalize the methods used in the Kaspi problem to the Fu-Yeung problem. As a result, we obtain the properties of optimal test channels for the minimum sum-rate function, a non-asymptotic converse bound and refined asymptotics for discrete memoryless sources. Since the successive refinement problem is a special case of the Fu-Yeung problem, as a byproduct, we obtain a non-asymptotic converse bound for the successive refinement problem, which is a strict generalization of the non-asymptotic converse bound for successively refinable sources (Zhou, Tan and Motani, 2017). Index TermsLossy source coding, multiple description coding problem, Non-asymptotic converse bound, Second-order asymptotics, Large Deviations, Moderate DeviationsThe authors are with the .sg. Part of this paper will be presented at Globecom 2017 [1], [2]. i.e., the second-order (cf. [13], [34], [35]), the large deviations (cf. [36], [37]) and the moderate deviations (cf. [38], [39])asymptotics. The converse proof of the second-order asymptotics follows by applying the Berry-Esseen theorem to the derived non-asymptotic converse bound and the achievability part relies on a type-covering lemma tailored to the Kaspi problem, proper uses of the Taylor's expansions, and the properties of the distortion-tilted information density. Since the Kaspi problem is a generalization of the lossy source coding problem and the lossy source coding problem with encoder and decoder side information, our second-order asymptotics for the Kaspi problem is a generalization of [13] and [40] for DMSes. We illustrate this point via numerical examples.We then extend the methods used in the Kaspi problem to the Fu-Yeung problem. First, we present the optimal test channels for the minimum sum-rate function. Subsequently,...

show abstract

On the Multiple Description Coding Problem with One Semi-Deterministic Distortion Measure

Zhou

Motani

2017

GLOBECOM 2017 - 2017 IEEE Global Communications Conference

View full text Add to dashboard Cite

Kaspi Problem Revisited: Non-Asymptotic Converse Bound and Second-Order Asymptotics

Cited by 5 publications

References 16 publications

On Finite Blocklength Lossy Source Coding

On Finite Blocklength Lossy Source Coding

Non-Asymptotic Converse Bounds and Refined Asymptotics for Two Source Coding Problems

On the Multiple Description Coding Problem with One Semi-Deterministic Distortion Measure

Contact Info

Product

Resources

About