Capacity-achieving sparse regression codes via spatial coupling

Sparse regression codes (SPARCs) are a recent coding technique for the AWGN channel where the codewords are linear combinations of columns of a design matrix. In a spatially coupled sparse regression code (SC-SPARC), the design matrix has a block-wise band-diagonal structure. SC-SPARCs can be decoded using an efficient Approximate Message Passing (AMP) decoder, whose performance can be predicted using a recursion known as state evolution. In this work, we obtain non-asymptotic bounds for the state evolution parameters. These bounds are used to describe the decoding progression in terms of the code parameters and the gap from capacity.