SPARCs for Unsourced Random Access

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 $\SNR$.

v3: Corrected some errors in Thm 2 and 4, v2: Major revision; Parts of this work have been presented at ISIT 2019 and ISIT 2020

References in corpus (4)

• Non-Bayesian Activity Detection, Large-Scale Fading Coefficient Estimation, and Unsourced Random Access with a Massive MIMO Receiver
• Probabilistic Reconstruction in Compressed Sensing: Algorithms, Phase Diagrams, and Threshold Achieving Matrices
• Massive MIMO Unsourced Random Access
• Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation

Cited by in corpus (15)

• Fundamental limits of many-user MAC with finite payloads and fading
• Sparse Regression Codes
• Coded Demixing for Unsourced Random Access
• Coded Compressed Sensing with Successive Cancellation List Decoding for Unsourced Random Access with Massive MIMO
• Near-Optimal Coding for Many-user Multiple Access Channels
• CHIRRUP: a practical algorithm for unsourced multiple access
• On Compressed Sensing of Binary Signals for the Unsourced Random Access Channel
• Mismatched Data Detection in Massive MU-MIMO
• Massive Access for Future Wireless Communication Systems
• An Exploration of the Heterogeneous Unsourced MAC
• Using List Decoding to Improve the Finite-Length Performance of Sparse Regression Codes
• Polar Coding and Sparse Spreading for Massive Unsourced Random Access
• Rigorous State Evolution Analysis for Approximate Message Passing with Side Information
• Sparse Kronecker-Product Coding for Unsourced Multiple Access
• Asynchronous Massive Access and Neighbor Discovery Using OFDMA