Capacity-achieving Sparse Superposition Codes via Approximate Message Passing Decoding
IEEE Transactions on Information Theory
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Rush, C., Greig, A., & Venkataramanan, R. (2017). Capacity-achieving Sparse Superposition Codes via Approximate Message Passing Decoding. IEEE Transactions on Information Theory, 63 (3), 1476-1500. https://doi.org/10.1109/TIT.2017.2649460
Sparse superposition codes were recently introduced by Barron and Joseph for reliable communication over the additive white Gaussian noise (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.
compressed sensing, sparse regression codes, capacity-achieving codes, AWGN channel, coded modulation, low-complexity decoding
This work was supported in part by a Marie Curie Career Integration Grant (Grant Agreement No. 631489). A. Greig was supported by an EPSRC Doctoral Training Award.
European Commission (631489)
External DOI: https://doi.org/10.1109/TIT.2017.2649460
This record's URL: https://www.repository.cam.ac.uk/handle/1810/262895