A Compressed Sensing Approach for Distribution Matching

TL;DR

This paper introduces a novel compressed sensing-based method for distribution matching that leverages sparsity and approximate message-passing, achieving near-optimal rates and low complexity for practical applications.

Contribution

It formulates distribution matching as a Bayesian inference problem using compressed sensing principles, introducing a low-complexity GAMP-based dematcher with asymptotic optimality.

Findings

GAMP dematcher achieves near-entropy rate performance.

Spatial coupling enhances asymptotic optimality.

Practical Hadamard-based operators are effective for implementation.

Abstract

In this work, we formulate the fixed-length distribution matching as a Bayesian inference problem. Our proposed solution is inspired from the compressed sensing paradigm and the sparse superposition (SS) codes. First, we introduce sparsity in the binary source via position modulation (PM). We then present a simple and exact matcher based on Gaussian signal quantization. At the receiver, the dematcher exploits the sparsity in the source and performs low-complexity dematching based on generalized approximate message-passing (GAMP). We show that GAMP dematcher and spatial coupling lead to asymptotically optimal performance, in the sense that the rate tends to the entropy of the target distribution with vanishing reconstruction error in a proper limit. Furthermore, we assess the performance of the dematcher on practical Hadamard-based operators. A remarkable feature of our proposed solution is the possibility to: i) perform matching at the symbol level (nonbinary); ii) perform joint channel coding and matching.