Successive Refinement for Lossy Compression of Individual Sequences

TL;DR

This paper investigates a successive refinement approach for lossy compression of individual sequences, establishing theoretical limits for finite-state encoders and proposing schemes for multiple description coding.

Contribution

It provides outer bounds for the rate region of finite-state encoders in successive refinement and extends achievability schemes to multiple description coding.

Findings

Outer bounds for finite-state encoder rate region established

Achievability schemes for successive refinement demonstrated

Extensions to multiple description coding proposed

Abstract

We consider the problem of successive-refinement coding for lossy compression of individual sequences, namely, compression in two stages, where in the first stage, a coarse description at a relatively low rate is sent from the encoder to the decoder, and in the second stage, additional coding rate is allocated in order to refine the description and thereby improve the reproduction. Our main result is in establishing outer bounds (converse theorems) for the rate region where we limit the encoders to be finite-state machines in the spirit of Ziv and Lempel's 1978 model.The matching achievability scheme is conceptually straightforward. We also consider the more general multiple description coding problem on a similar footing and propose achievability schemes that are analogous to the well-known El Gamal-Cover and the Zhang-Berger achievability schemes of memoryless sources and additive distortion measures.