Wyner-Ziv Coding Based on Multidimensional Nested Lattices

TL;DR

This paper explores multi-dimensional nested lattice coding for Wyner-Ziv source coding, providing theoretical rate-distortion analysis and practical low-complexity code design that outperform existing methods.

Contribution

It introduces a new multi-dimensional nested lattice coding framework for Wyner-Ziv coding, with improved performance and reduced complexity compared to prior two-dimensional lattice approaches.

Findings

Higher rate-distortion efficiency under high-resolution assumptions.

New upper bound on rate-distortion using theta series derivatives.

Reduced complexity without Slepian-Wolf coding stage.

Abstract

Distributed source coding (DSC) addresses the compression of correlated sources without communication links among them. This paper is concerned with the Wyner-Ziv problem: coding of an information source with side information available only at the decoder in the form of a noisy version of the source. Both the theoretical analysis and code design are addressed in the framework of multi-dimensional nested lattice coding (NLC). For theoretical analysis, accurate computation of the rate-distortion function is given under the high-resolution assumption, and a new upper bound using the derivative of the theta series is derived. For practical code design, several techniques with low complexity are proposed. Compared to the existing Slepian-Wolf coded nested quantization (SWC-NQ) for Wyner-Ziv coding based on one or two-dimensional lattices, our proposed multi-dimensional NLC can offer better performance at arguably lower complexity, since it does not require the second stage of Slepian-Wolf coding.