An achievable rate-distortion region for the multiple descriptions problem

Shirani, Farhad; Pradhan, S. Sandeep

doi:10.1109/isit.2014.6874898

Cited by 5 publications

(39 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Fano inequality type bounds will enables us upper bound additional information that needs to be communicated via outer codes. We leverage the novel technique of interleaving devised by Shirani and Pradhan [2] in the related problem of distributed source coding. Therein, the authors [2] proposed a pure source coding scheme to communicate information streams of different B-Ls to enable the decoder reconstruct quantized versions of the distributed sources.…”

Section: Rxmentioning

confidence: 99%

“…We leverage the novel technique of interleaving devised by Shirani and Pradhan [2] in the related problem of distributed source coding. Therein, the authors [2] proposed a pure source coding scheme to communicate information streams of different B-Ls to enable the decoder reconstruct quantized versions of the distributed sources. The common thread between the problem studied herein and [2] is the presence of the LMC.…”

Section: Rxmentioning

confidence: 99%

See 1 more Smart Citation

Communicating Correlated Sources Over MAC and Interference Channels I: Separation-Based Schemes

Padakandla

2020

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

We consider the two scenarios of communicating a pair S 1 , S 2 of distributed correlated sources over 2−user multiple access (MAC) and interference channels (IC) respectively. While in the MAC problem, the receiver intends to reconstruct both sources losslessly, in the IC problem, receiver j intends to reconstruct S j losslessly. We undertake a Shannon theoretic study and focus on achievability, i.e., characterizing sufficient conditions. In the absence of a Gaćs-Körner-Witsenhausen common part, the current known single-letter (S-L) coding schemes are constrained to choosing X jt -the symbol input on the channel by encoder j at time t -based only S jt -the source symbol observed by it, at time t, resulting in the pmf p X1X2 of the inputs X 1 , X 2 constrained to the S-L long Markov Chain (LMC) X 1 − S 1 − S 2 − X 2 . Taking the lead of Dueck's example [1], we recognize that the latter constraint is debilitating, leading to sub-optimality of S-L coding schemes. The goal of our work is to design a coding scheme wherein (i) the choice of X jt is based on multiple source symbols S l j , and is yet ii) amenable to performance characterization via S-L expressions. In this article, we present the first part of our findings. We propose a new separation-based coding scheme comprising of (i) a fixed block-length (B-L) code that enables choice of X jt based on a generic number l of source symbols, thus permitting correlation of the input symbols X 1 , X 2 through a multiletter LMC X 1 − S l 1 − S l 2 − X 2 , (ii) arbitrarily large B-L codes superimposed on multiple sub-blocks of the fixed B-L code that communicate the rest of the information necessary for source reconstruction at the decoder(s), and (iii) a multiplexing unit based on the interleaving technique [2] that ensures the latter codes of arbitrarily large B-L experience a memoryless channel. This careful stitching of S-L coding techniques enables us to devise a multi-letter coding scheme that permits characterization of sufficient conditions via a S-L expression. We prove that the derived inner bound is strictly larger than the current known largest inner bounds for both the MAC and IC problems.Since the proposed coding scheme is inherently separation based, the derived inner bound does not subsume the current known largest. In the second part of our work, we propose to enlarge the inner bound derived in this article by incorporating the technique of inducing source correlation onto channel inputs [3].

show abstract

Section: Rxmentioning

confidence: 99%

Section: Rxmentioning

confidence: 99%

Communicating Correlated Sources Over MAC and Interference Channels I: Separation-Based Schemes

Padakandla

2020

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

show abstract

“…and the rest of the random variables in Theorem 1 to constants. It is easy to verify that the rate-distortion region given in (27) is achievable by the CMS scheme using the above joint distribution for the auxiliary random variables and by choosing the auxiliary rate R 123 = I(X; V 123 ).…”

Section: B General Sources and Distortion Measuresmentioning

confidence: 99%

“…We will briefly discuss the extension towards the end of the proof. Towards proving (ii), we consider one particular boundary point of (27) and show that this cannot be achieved by the VKG encoding scheme. Let > 0 and D 1 , D 2 and D 12 be fixed.…”

Section: B General Sources and Distortion Measuresmentioning

confidence: 99%

“…The CMS scheme is only one of the several possible generalizations of the ZB scheme to L-descriptions. The fundamental idea of introducing structured codes and controlled redundancy for L−channel multiple descriptions problem is not new and has been explored in several publications in the past, including [8], [7], [17], [27] and some of these schemes have been shown to outperform VKG for certain sources and distortion measures. However, to the best of our knowledge, for a Gaussian source, under MSE, CMS is the only generalization of the VKG scheme that achieves a strictly larger rate-distortion region.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Combinatorial Message Sharing and a New Achievable Region for Multiple Descriptions

Viswanatha

Akyol

Rose

2016

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

Abstract-This paper presents a new achievable rate-distortion region for the general L channel multiple descriptions problem. A well known general region for this problem is due to Venkataramani, Kramer and Goyal (VKG) [1]. Their encoding scheme is an extension of the El-Gamal-Cover (EC) and ZhangBerger (ZB) coding schemes to the L channel case and includes a combinatorial number of refinement codebooks, one for each subset of the descriptions. As in ZB, the scheme also allows for a single common codeword to be shared by all descriptions. This paper proposes a novel encoding technique involving 'Combinatorial Message Sharing' (CMS), where every subset of the descriptions may share a distinct common message. This introduces a combinatorial number of shared codebooks along with the refinement codebooks of [1]. These shared codebooks provide a more flexible framework to trade-off redundancy across the messages for resilience to descriptions loss. We derive an achievable rate-distortion region for the proposed technique, and show that it subsumes the VKG region for general sources and distortion measures. We further show that CMS provides a strict improvement of the achievable region for any source and distortion measures for which some 2-description subset is such that ZB achieves points outside the EC region. We then show a more surprising result: CMS outperforms VKG for a general class of sources and distortion measures, including scenarios where the ZB and EC regions coincide for all 2-description subsets. In particular, we show that CMS strictly improves on VKG, for the L−channel quadratic Gaussian MD problem, for all L ≥ 3, despite the fact that the EC region is complete for the corresponding 2-descriptions problem. Consequently, the 'correlated quantization' scheme (an extreme special case of VKG), that has been proven to be optimal for several crosssections of the L−channel quadratic Gaussian MD problem, is strictly suboptimal in general. Using the encoding principles derived, we show that the CMS scheme achieves the complete rate-distortion region for several asymmetric cross-sections of the L−channel quadratic Gaussian MD problem.

show abstract