Erasure Multiple Descriptions

TL;DR

This paper investigates the binary erasure multiple descriptions problem, proposing coding schemes and bounds that optimize distortion under average and worst-case criteria, with applications to Gaussian sources and the CEO problem.

Contribution

It introduces achievability schemes and optimality results for binary erasure multiple descriptions, and develops a layered coding framework with proven optimality for certain Gaussian cases.

Findings

Achievability schemes based on random binning and MDS codes are optimal for the considered distortion criteria.

A layered coding framework is proposed and shown to be optimal for symmetric scalar Gaussian multiple descriptions.

A new outer bound for multi-terminal source coding and a tight lower bound for the robust binary erasure CEO problem are established.

Abstract

We consider a binary erasure version of the n-channel multiple descriptions problem with symmetric descriptions, i.e., the rates of the n descriptions are the same and the distortion constraint depends only on the number of messages received. We consider the case where there is no excess rate for every k out of n descriptions. Our goal is to characterize the achievable distortions D_1, D_2,...,D_n. We measure the fidelity of reconstruction using two distortion criteria: an average-case distortion criterion, under which distortion is measured by taking the average of the per-letter distortion over all source sequences, and a worst-case distortion criterion, under which distortion is measured by taking the maximum of the per-letter distortion over all source sequences. We present achievability schemes, based on random binning for average-case distortion and systematic MDS (maximum distance separable) codes for worst-case distortion, and prove optimality results for the corresponding achievable distortion regions. We then use the binary erasure multiple descriptions setup to propose a layered coding framework for multiple descriptions, which we then apply to vector Gaussian multiple descriptions and prove its optimality for symmetric scalar Gaussian multiple descriptions with two levels of receivers and no excess rate for the central receiver. We also prove a new outer bound for the general multi-terminal source coding problem and use it to prove an optimality result for the robust binary erasure CEO problem. For the latter, we provide a tight lower bound on the distortion for \ell messages for any coding scheme that achieves the minimum achievable distortion for k messages where k is less than or equal to \ell.