Quasi Linear Codes: Application to Point-to-Point and Multi-Terminal Source Coding

TL;DR

This paper introduces Quasi Linear Codes (QLC), a new structured code ensemble that improves rate-distortion performance in multi-terminal source coding problems, especially in the multiple-descriptions scenario.

Contribution

The paper proposes Quasi Linear Codes, a novel code structure that offers better achievable rate-distortion regions in multi-terminal source coding, including the multiple-descriptions problem.

Findings

QLC provides improved achievable rate-distortion regions.

Application of QLC yields better performance in the multiple-descriptions problem.

Derived inner bounds strictly contain previous known regions.

Abstract

A new ensemble of structured codes is introduced. These codes are called Quasi Linear Codes (QLC). The QLC's are constructed by taking subsets of linear codes. They have a looser structure compared to linear codes and are not closed under addition. We argue that these codes provide gains in terms of achievable Rate-Distortions (RD) in different multi-terminal source coding problems. We derive the necessary covering bounds for analyzing the performance of QLC's. We then consider the Multiple-Descriptions (MD) problem, and prove through an example that the application of QLC's gives an improved achievable RD region for this problem. Finally, we derive an inner bound to the achievable RD region for the general MD problem which strictly contains all of the previous known achievable regions.