Capacity-achieving Sparse Superposition Codes via Approximate Message Passing Decoding
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Publication Date
2017-01-09Journal Title
IEEE Transactions on Information Theory
ISSN
0018-9448
Publisher
IEEE
Volume
63
Issue
3
Pages
1476-1500
Language
English
Type
Article
This Version
AM
Metadata
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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
Abstract
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.
Keywords
compressed sensing, sparse regression codes, capacity-achieving codes, AWGN channel, coded modulation, low-complexity decoding
Sponsorship
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.
Funder references
European Commission (631489)
EPSRC (1355086)
Identifiers
External DOI: https://doi.org/10.1109/TIT.2017.2649460
This record's URL: https://www.repository.cam.ac.uk/handle/1810/262895
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