Spatially Coupled Sparse Regression Codes with Sliding Window AMP Decoding

Abstract

We analyze the performance of spatially coupled sparse regression codes (SC-SPARCs) over the AWGN channel with a sliding window approximate message passing (AMP) decoder. In an SC-SPARC, the codewords are sparse linear combinations of columns of a Gaussian matrix that has a block-wise band-diagonal structure. In this paper we introduce and motivate the sliding-window AMP decoder for SC-SPARCs, and present the first steps towards a fully rigorous proof that the SC-SPARCs with sliding window AMP decoding are asymptotically capacity-achieving. We also provide numerical simulation results demonstrating the error performance of the sliding window AMP decoder at finite code lengths.