Approximate Message Passing under Finite Alphabet Constraints

TL;DR

This paper introduces an iterative message passing algorithm tailored for Basis Pursuit De-Noising problems with signals from finite alphabets, leveraging prior knowledge to enhance recovery performance in compressive sampling.

Contribution

The paper presents a novel message passing algorithm that incorporates discrete signal priors, improving sparse signal recovery in finite alphabet BPDN problems over existing methods.

Findings

Significant performance gains over linear programming approaches.

Enhanced recovery accuracy with prior knowledge compared to without prior.

Effective in compressive sampling of analogue signals.

Abstract

In this paper we consider Basis Pursuit De-Noising (BPDN) problems in which the sparse original signal is drawn from a finite alphabet. To solve this problem we propose an iterative message passing algorithm, which capitalises not only on the sparsity but by means of a prior distribution also on the discrete nature of the original signal. In our numerical experiments we test this algorithm in combination with a Rademacher measurement matrix and a measurement matrix derived from the random demodulator, which enables compressive sampling of analogue signals. Our results show in both cases significant performance gains over a linear programming based approach to the considered BPDN problem. We also compare the proposed algorithm to a similar message passing based algorithm without prior knowledge and observe an even larger performance improvement.