An Achievable Rate-Distortion Region for Multiple Descriptions Source Coding Based on Coset Codes

TL;DR

This paper introduces a new unified coding strategy for multiple descriptions source coding that combines structured and unstructured coding techniques, leading to a strictly larger achievable rate-distortion region than previous methods.

Contribution

It develops a novel unified coding framework using structured codes, improving upon existing unstructured schemes and demonstrating strict rate-distortion benefits for more than two descriptions.

Findings

Structured coding yields strict RD improvements for more than two descriptions.

The new RD region strictly contains all previously known achievable regions.

Structured binning and quantizers are essential for multi-description coding beyond two descriptions.

Abstract

We consider the problem of multiple descriptions (MD) source coding and propose new coding strategies involving both unstructured and structured coding layers. Previously, the most general achievable rate-distortion (RD) region for the $l$-descriptions problem was the Combinatorial Message Sharing with Binning (CMSB) region. The CMSB scheme utilizes unstructured quantizers and unstructured binning. In the first part of the paper, we show that this strategy can be improved upon using more general unstructured quantizers and a more general unstructured binning method. In the second part, structured coding strategies are considered. First, structured coding strategies are developed by considering specific MD examples involving three or more descriptions. We show that application of structured quantizers results in strict RD improvements when there are more than two descriptions. Furthermore, we show that structured binning also yields improvements. These improvements are in addition to the ones derived in the first part of the paper. This suggests that structured coding is essential when coding over more than two descriptions. Using the ideas developed through these examples we provide a new unified coding strategy by considering several structured coding layers. Finally, we characterize its performance in the form of an inner bound to the optimal rate-distortion region using computable single-letter information quantities. The new RD region strictly contains all of the previous known achievable regions.