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Optimizing the Finite Length Performance of Sparse Superposition Codes

Sparse superposition codes are a recent class of codes introduced by Barron and Joseph for efficient communication over the AWGN channel. With an appropriate power allocation, these codes have been shown to be asymptotically capacity-achieving with computationally feasible decoding. However, a direct implementation of the capacity-achieving construction does not give good finite length error performance, and has unnecessarily high computational complexity. In this paper, we consider sparse superposition codes with approximate message passing (AMP) decoding, and describe a variety of techniques to improve their finite length performance and decrease computational complexity. These include using implicit Walsh-Hadamard design matrices, optimizing SPARC power allocations and codebook parameters, and estimating a critical decoding parameter online instead of pre-computation. Finally we compare the error performance of AMP-decoded sparse superposition codes with coded modulation using LDPC codes from the WiMAX standard.