Unsourced Multiuser Sparse Regression Codes achieve the Symmetric MAC Capacity

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. Recently a concatenated coding construction for U-RA on the AWGN channel was presented, 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. In this work we show that this 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. Additionally, we calculate the algorithmic threshold, that is a bound on the sum-rate up to which the inner decoding can be done reliably with the low-complexity AMP algorithm.

arXiv comment7 pages, submitted to ISIT 2020. arXiv admin note: substantial text overlap with arXiv:1901.06234

References in corpus (9)

• Message Passing Algorithms for Compressed Sensing
• The dynamics of message passing on dense graphs, with applications to compressed sensing
• Asymptotic Analysis of MAP Estimation via the Replica Method and Applications to Compressed Sensing
• Probabilistic Reconstruction in Compressed Sensing: Algorithms, Phase Diagrams, and Threshold Achieving Matrices
• Capacity-achieving Sparse Superposition Codes via Approximate Message Passing Decoding
• Approximate message-passing decoder and capacity-achieving sparse superposition codes
• Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation
• Sparse Regression Codes
• Grant-Free Massive Random Access With a Massive MIMO Receiver

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