Multi-User SR-LDPC Codes

This article introduces a novel non-orthogonal multiple access (NOMA) scheme for coordinated uplink channels. The scheme builds on the recently proposed sparse-regression low-density parity-check (SR-LDPC) code, and extends the underlying notions to scenarios with many concurrent users. The resulting scheme, called Multi-User SR-LDPC (MU-SR-LDPC) coding, consists of each user transmitting its own SR-LDPC codeword using a unique sensing matrix in conjunction with a characteristic outer LDPC code. To recover the sent information, the decoder jointly processes the received signals using a low-complexity and highly-parallelizable AMP-BP algorithm. At finite blocklengths (FBL), MU-SR-LDPC codes are shown to achieve a target BER at a higher spectral efficiency than baseline orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA) schemes with similar computational complexity. Furthermore, MU-SR-LDPC codes are shown to match the performance of maximum a posteriori (MAP) decoding in certain regimes. For certain blocklengths and a sufficiently high number of users, MU-SR-LDPC codes may achieve a higher spectral efficiency than the approximate FBL capacity of the effective single-user Gaussian channel seen by each user in a comparable OMA scheme. Results are supported by numerical simulations.