# SPARCs for Unsourced Random Access

## TL;DR

This paper introduces a concatenated coding scheme using SPARCs and an outer code for unsourced random access over AWGN channels, achieving near-capacity performance with a modified AMP decoder.

## Contribution

It proposes a novel concatenated coding construction with a modified AMP decoder for U-RA, extending SPARC optimality to multiuser scenarios and providing an SNR optimization method.

## Key findings

- Achieves vanishing error probability at rates up to Shannon capacity.
- Extends SPARC optimality from point-to-point to multiuser U-RA.
- Provides an SNR minimization algorithm for power allocation.

## Abstract

Unsourced random-access (U-RA) is a type of grant-free random access with a virtually unlimited number of users, of which only a certain number $K_a$ are active on the same time slot. Users employ exactly the same codebook, and the task of the receiver is to decode the list of transmitted messages. We present a concatenated coding construction for U-RA on the AWGN channel, in which a sparse regression code (SPARC) is used as an inner code to create an effective outer OR-channel. Then an outer code is used to resolve the multiple-access interference in the OR-MAC. We propose a modified version of the approximate message passing (AMP) algorithm as an inner decoder and give a precise asymptotic analysis of the error probabilities of the AMP decoder and of a hypothetical optimal inner MAP decoder. This analysis shows that the concatenated construction can achieve a vanishing per-user error probability in the limit of large blocklength and a large number of active users at sum-rates up to the symmetric Shannon capacity, i.e. as long as $K_aR < 0.5\log_2(1+K_a\SNR)$. This extends previous point-to-point optimality results about SPARCs to the unsourced multiuser scenario. Furthermore, we give an optimization algorithm to find the power allocation for the inner SPARC code that minimizes the required $\SNR$.