Coded Compressed Sensing with List Recoverable Codes for the Unsourced Random Access

TL;DR

This paper introduces a novel coded compressed sensing scheme for unsourced random access that employs list recoverable codes, significantly enhancing performance over traditional tree codes, especially in scenarios with fewer active users.

Contribution

It replaces the outer tree code with list recoverable codes capable of correcting errors, providing practical constructions and demonstrating improved performance in fading channels.

Findings

Performance improves by 7-10 dB with list recoverable codes

Two practical outer code constructions are proposed

Reed-Solomon based scheme outperforms tree code for fewer than 200 users

Abstract

We consider a coded compressed sensing approach for the unsourced random access and replace the outer tree code proposed by Amalladinne et al. with the list recoverable code capable of correcting t errors. A finite-length random coding bound for such codes is derived. The numerical experiments in the single antenna quasi-static Rayleigh fading MAC show that transition to list recoverable codes correcting t errors improves the performance of coded compressed sensing scheme by 7-10 dB compared to the tree code-based scheme. We propose two practical constructions of outer codes. The first is a modification of the tree code. It utilizes the same code structure, and a key difference is a decoder capable of correcting up to t errors. The second is based on the Reed-Solomon codes and Guruswami-Sudan list decoding algorithm. The first scheme provides an energy efficiency very close to the random coding bound when the decoding complexity is unbounded. But for the practical parameters, the second scheme is better and improves the performance of a tree code-based scheme when the number of active users is less than 200.