Joint Source-Channel Vector Quantization for Compressed Sensing

TL;DR

This paper develops and analyzes joint source-channel vector quantization schemes for compressed sensing measurements, introducing optimal and low-complexity designs with theoretical bounds and practical algorithms.

Contribution

It presents a new framework for optimal JSCC of CS measurements, including the design of channel-optimized VQ schemes and low-complexity multi-stage VQ methods.

Findings

Theoretical lower-bound on MSE performance derived.

Proposed iterative algorithms for encoder-decoder design.

Simulation results show improved performance over existing quantizers.

Abstract

We study joint source-channel coding (JSCC) of compressed sensing (CS) measurements using vector quantizer (VQ). We develop a framework for realizing optimum JSCC schemes that enable encoding and transmitting CS measurements of a sparse source over discrete memoryless channels, and decoding the sparse source signal. For this purpose, the optimal design of encoder-decoder pair of a VQ is considered, where the optimality is addressed by minimizing end-to-end mean square error (MSE). We derive a theoretical lower-bound on the MSE performance, and propose a practical encoder-decoder design through an iterative algorithm. The resulting coding scheme is referred to as channel- optimized VQ for CS, coined COVQ-CS. In order to address the encoding complexity issue of the COVQ-CS, we propose to use a structured quantizer, namely low complexity multi-stage VQ (MSVQ). We derive new encoding and decoding conditions for the MSVQ, and then propose a practical encoder-decoder design algorithm referred to as channel-optimized MSVQ for CS, coined COMSVQ-CS. Through simulation studies, we compare the proposed schemes vis-a-vis relevant quantizers.