Sparse Regression Codes exploit Multi-User Diversity without CSI

We study sparse regression codes (SPARC) for multiple access channels with multiple receive antennas, in non-coherent flat fading channels. We propose a novel practical decoder, referred to as maximum likelihood matching pursuit (MLMP), which greedily finds the support of the codewords of users with partial maximum likelihood metrics. As opposed to the conventional successive-cancellation based greedy algorithms, MLMP works as a successive-combining energy detector. We also propose MLMP modifications to improve the performance at high code rates. Our studies in short block lengths show that, even without any channel state information, SPARC with MLMP decoder achieves multi-user diversity in some scenarios, giving better error performance with multiple users than that of the corresponding single-user case. We also show that SPARC with MLMP performs better than conventional sparse recovery algorithms and pilot-aided transmissions with polar codes.