A Hybrid Approach to Coded Compressed Sensing where Coupling Takes Place via the Outer Code

TL;DR

This paper introduces a hybrid coded compressed sensing scheme combining block diagonal sensing matrices with a dynamic denoiser, enhancing scalability and performance for unsourced random access.

Contribution

It proposes a novel architecture integrating AMP and belief propagation with block diagonal sensing matrices for improved scalability and efficiency in coded compressed sensing.

Findings

Achieves good performance at low complexity

Scales to larger problem dimensions

Supported by numerical simulation results

Abstract

This article seeks to advance coded compressed sensing (CCS) as a practical scheme for unsourced random access. The original CCS algorithm features a concatenated structure where an inner code is tasked with support recovery, and an outer tree code conducts message disambiguation. Recently, a link between CCS and sparse regression codes was established, leading to the application of approximate message passing (AMP) to CCS. This connection was subsequently strengthened by integrating AMP and belief propagation on the outer code through a dynamic denoiser. Along these lines, this work shows how block diagonal sensing matrices akin to those used in traditional CCS, together with the aforementioned dynamic denoiser, form an effective means to get good performance at low-complexity. This novel architecture can be used to scale this scheme to dimensions that were previously impractical. Findings are supported by numerical simulations.