Capacity-achieving Sparse Superposition Codes via Approximate Message Passing Decoding
This work addresses efficient decoding for communication systems, offering a novel method with practical improvements but is incremental relative to existing sparse superposition codes.
The authors tackled reliable communication over the AWGN channel by proposing an approximate message passing decoder for sparse superposition codes, achieving asymptotic channel capacity with linear decoding complexity and demonstrating improved performance at finite blocklengths through power allocation and Hadamard matrices.
Sparse superposition codes were recently introduced by Barron and Joseph for reliable communication over the AWGN channel at rates approaching the channel capacity. The codebook is defined in terms of a Gaussian design matrix, and codewords are sparse linear combinations of columns of the matrix. In this paper, we propose an approximate message passing decoder for sparse superposition codes, whose decoding complexity scales linearly with the size of the design matrix. The performance of the decoder is rigorously analyzed and it is shown to asymptotically achieve the AWGN capacity with an appropriate power allocation. Simulation results are provided to demonstrate the performance of the decoder at finite blocklengths. We introduce a power allocation scheme to improve the empirical performance, and demonstrate how the decoding complexity can be significantly reduced by using Hadamard design matrices.