Wyner-Ziv Coding in the Real Field Based on BCH-DFT Codes

TL;DR

This paper introduces a novel framework for distributed lossy source coding using real-number codes, specifically DFT codes, which improves correlation modeling and error compensation in Wyner-Ziv coding.

Contribution

It proposes a new approach that compresses correlated sources before quantization, enhancing correlation modeling and error correction in Wyner-Ziv coding with real-number codes.

Findings

Mean-squared error is close to the quantization error level.

The framework is suitable for low-delay communications.

Extension to noisy channels with joint source-channel coding.

Abstract

We show how real-number codes can be used to compress correlated sources and establish a new framework for distributed lossy source coding, in which we quantize compressed sources instead of compressing quantized sources. This change in the order of binning and quantization blocks makes it possible to model correlation between continuous-valued sources more realistically and compensate for the quantization error when the sources are completely correlated. We focus on the asymmetric case, i.e., lossy source coding with side information at the decoder, also known as Wyner-Ziv coding. The encoding and decoding procedures are described in detail for discrete Fourier transform (DFT) codes, both for syndrome- and parity-based approaches. We also extend the parity-based approach to the case where the transmission channel is noisy and perform distributed joint source-channel coding in this context. The proposed system is well suited for low-delay communications. Furthermore, the mean-squared reconstruction error (MSE) is shown to be less than or close to the quantization error level, the ideal case in coding based on binary codes.