Fundamental limits of many-user MAC with finite payloads and fading

Abstract

Consider a (multiple-access) wireless communication system where users are connected to a unique base station over a shared-spectrum radio links. Each user has a fixed number $k$ of bits to send to the base station, and his signal gets attenuated by a random channel gain (quasi-static fading). In this paper we consider the many-user asymptotics of Chen-Chen-Guo'2017, where the number of users grows linearly with the blocklength. Differently, though, we adopt a per-user probability of error (PUPE) criterion (as opposed to classical joint-error probability criterion). Under PUPE the finite energy-per-bit communication is possible, and we are able to derive bounds on the tradeoff between energy and spectral efficiencies. We reconfirm the curious behaviour (previously observed for non-fading MAC) of the possibility of almost perfect multi-user interference (MUI) cancellation for user densities below a critical threshold. Further, we demonstrate the suboptimality of standard solutions such as orthogonalization (i.e., TDMA/FDMA) and treating interference as noise (i.e. pseudo-random CDMA without multi-user detection). Notably, the problem treated here can be seen as a variant of support recovery in compressed sensing for the unusual definition of sparsity with one non-zero entry per each contiguous section of $2^k$ coordinates. This identifies our problem with that of the sparse regression codes (SPARCs) and hence our results can be equivalently understood in the context of SPARCs with sections of length $2^{100}$. Finally, we discuss the relation of the almost perfect MUI cancellation property and the replica-method predictions.

arXiv comment34 pages, accepted for publication in IEEE Transactions on Information Theory

References in corpus (16)

• Message Passing Algorithms for Compressed Sensing
• The dynamics of message passing on dense graphs, with applications to compressed sensing
• SPARCs for Unsourced Random Access
• Information theoretic bounds for Compressed Sensing
• Approximate message-passing decoder and capacity-achieving sparse superposition codes
• Massive MIMO Unsourced Random Access
• The Mutual Information in Random Linear Estimation
• Sparse Regression Codes
• Capacity-achieving Spatially Coupled Sparse Superposition Codes with AMP Decoding
• The Error Probability of Sparse Superposition Codes with Approximate Message Passing Decoding
• Concise Derivation of Complex Bayesian Approximate Message Passing via Expectation Propagation
• A Coded Compressed Sensing Scheme for Uncoordinated Multiple Access
• Compressed Sensing of Approximately-Sparse Signals: Phase Transitions and Optimal Reconstruction
• CHIRRUP: a practical algorithm for unsourced multiple access
• Statistical physics and approximate message-passing algorithms for sparse linear estimation problems in signal processing and coding theory
• On the Fundamental Limits of MIMO Massive Multiple Access Channels

Cited by in corpus (9)

• Gaussian Multiple and Random Access in the Finite Blocklength Regime
• Joint Device Activity Detection, Channel Estimation and Signal Detection for Massive Grant-free Access via BiGAMP
• Near-Optimal Coding for Many-user Multiple Access Channels
• Massive Access for Future Wireless Communication Systems
• Uplink Grant-Free Random Access Solutions for URLLC services in 5G New Radio
• On the Fundamental Limits of MIMO Massive Access Communication
• One-Shot Messaging at Any Load Through Random Sub-Channeling in OFDM
• Many-User Multiple Access with Random User Activity: Achievability Bounds and Efficient Schemes
• Energy-efficiency of Massive Random Access with Individual Codebook