Generalized Sparse Regression Codes for Short Block Lengths

Sparse Regression Code (SPARC) connects the sparse signal recovery framework with the error control coding techniques. In this paper, we focus on improving the block error performance of SPARC in short block length regime over the AWGN channel. Towards that, we introduce suitable candidates for dictionary matrices in real and complex fields using Gold sequences and mutually unbiased bases (MUB). We propose two generalizations of SPARC (GSPARC), develop a greedy decoder called Match and Decode (MAD) algorithm, and provide its analytical noiseless recovery guarantees. We propose a parallel greedy search technique called parallel MAD (PMAD) to improve performance. We describe the applicability of GSPARC with PMAD decoder for multi-user channels, providing a non-orthogonal multiple access scheme. We present numerical results comparing the block error rate (BLER) performance of the proposed algorithms for GSPARC in AWGN channels in the short block length regime. The PMAD decoder gives better BLER than the approximate message-passing decoder for SPARC. GSPARC with PMAD gives comparable and competitive BLER performance compared to other existing codes. In multi-user channels, GSPARC with PMAD decoder outperforms the sphere packing lower bounds of an orthogonal multiple access scheme with the same spectral efficiency.