Approximate Support Recovery using Codes for Unsourced Multiple Access

TL;DR

This paper introduces low-complexity algorithms for approximate support recovery of sparse signals from noisy measurements by adapting techniques from unsourced multiple access, offering a practical alternative to traditional compressed sensing methods.

Contribution

It develops two novel decoding algorithms with significantly reduced computational complexity for support recovery in large-scale sparse signals, inspired by multiple access coding strategies.

Findings

Algorithms achieve lower complexity than AMP-MMSE.

Support recovery performance is comparable with slight performance trade-offs.

Highlights the role of multiple access concepts in measurement design.

Abstract

We consider the approximate support recovery (ASR) task of inferring the support of a $K$-sparse vector ${\bf x} \in \mathbb{R}^n$ from $m$ noisy measurements. We examine the case where $n$ is large, which precludes the application of standard compressed sensing solvers, thereby necessitating solutions with lower complexity. We design a scheme for ASR by leveraging techniques developed for unsourced multiple access. We present two decoding algorithms with computational complexities $\mathcal{O}(K^2 \log n+K \log n \log \log n)$ and $\mathcal{O}(K^3 +K^2 \log n+ K \log n \log \log n)$ per iteration, respectively. When $K \ll n$, this is much lower than the complexity of approximate message passing with a minimum mean squared error denoiser% (AMP-MMSE) ,which requires $\mathcal{O}(mn)$ operations per iteration. This gain comes at a slight performance cost. Our findings suggest that notions from multiple access %such as spreading, matched filter receivers and codes can play an important role in the design of measurement schemes for ASR.