Unsourced Random Access with Coded Compressed Sensing: Integrating AMP and Belief Propagation

Abstract

Sparse regression codes with approximate message passing (AMP) decoding have gained much attention in recent times. The concepts underlying this coding scheme extend to unsourced random access with coded compressed sensing (CCS), as first demonstrated by Fengler, Jung, and Caire. Specifically, their approach employs a concatenated coding framework with an inner AMP decoder followed by an outer tree decoder. In their original implementation, these two components work independently of each other, with the tree decoder acting on the static output of the AMP decoder. This article introduces a novel framework where the inner AMP decoder and the outer tree decoder operate in tandem, dynamically passing information back and forth to take full advantage of the underlying CCS structure. This scheme necessitates the redesign of the tree code as to enable belief propagation in a computationally tractable manner. The enhanced architecture exhibits significant performance benefits over a range of system parameters. The error performance of the proposed scheme can be accurately predicted through a set of equations, known as state evolution of AMP. These findings are supported both analytically and through numerical methods.

Improved bounds for the many-user MAC

“…In the context of massive multiple access, AMP algorithms have found applications in unsourced MAC [10,31], but also to provide achievability bounds in the many-user asymptotics [5,15]. In this work we build upon [5,15] to provide new, improved and computable achievability bounds for the two channels considered.…”

“…In this paper we use scalar AMP idea from [5] and spatial coupling from [15] to obtain improved achievability bounds that are computable for moderate values of k (like k = 100 bits that is a standard in massive and unsourced MAC [3,8,31]).…”

Approximate Support Recovery using Codes for Unsourced Multiple Access

“…Thenceforth, there has been significant research interest in the design of practical coding schemes that exhibit low decoding complexity and perform close to these achievability benchmarks. The coding schemes developed for URA can be broadly categorized into two groups: schemes built on traditional channel codes (e.g., [14], [15], [20], [21]), and schemes that utilize the coded compressed sensing (CCS) framework (e.g., [12], [16], [22], [23]).…”

A Hierarchical Stitching Algorithm for Coded Compressed Sensing

“…In the n th time slot, if the candidate tree contains only one path, then the codeword of a user can be recovered. Instead of using the hard stitching decisions in [1], a recent advance in [13] is to use soft stitching decisions based on LDPC codes (with parity sub-blocks) so that the sub-CS problem and the stitching problem can be iteratively solved. However, as pointed out in [14], there might be several codewords on the same factor graph within the LDPC code, and that leads to negative impacts for the application of belief propagation on the LDPC code.…”