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Sparse superposition codes were recently introduced by Barron and Joseph for reliable communication over the AWGN channel at rates approaching the channel capacity.
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A. Joseph and A. R. Barron, “Fast sparse superposition codes have near exponential error probability for R < 𝒞 {R}<\mathcal{C} ,” IEEE Trans. Inf. Theory
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A. Montanari, “Graphical models concepts in compressed sensing,” in Compressed Sensing
2012
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M. Bayati and A. Montanari, “The LASSO risk for Gaussian matrices,” IEEE Trans. Inf. Theory
2012
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2012
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S. Som and P. Schniter, “Compressive imaging using approximate message passing and a Markov-tree prior,” IEEE Trans. Signal Processing
2012
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J. Barbier and F. Krzakala, “Replica analysis and approximate message passing decoder for sparse superposition codes,” in Proc. IEEE Int. Symp. Inf. Theory
2014
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Online: https://arxiv.org/abs/1411.0187
Y. Yan, L. Liu, C. Ling, and X. Wu, “Construction of capacity-achieving lattice codes: Polar lattices,” 2014 · 2014
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Online: https://arxiv.org/abs/1503.08040
J. Barbier and F. Krzakala, “Approximate message-passing decoder and capacity-achieving sparse superposition codes,” 2015 · 2015
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