Capacity-Achieving Sparse Superposition Codes via Approximate Message Passing Decoding
Capacity-Achieving Sparse Superposition Codes via Approximate Message Passing Decoding
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DOI：
10.1109/tit.2017.2649460
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发表时间：
2017-03-01
影响因子：
2.5
通讯作者：
Venkataramanan, Ramji
中科院分区：
文献类型：
--
作者：
Rush, Cynthia;Greig, Adam;Venkataramanan, Ramji
巴伦和约瑟夫最近提出了稀疏叠加码，用于在加性白色高斯噪声（AWGN）信道上以接近信道容量的速率进行可靠通信。码本是根据高斯设计矩阵来定义的，并且码字是矩阵的列的稀疏线性组合。在本文中，我们提出了一个近似的消息传递解码器的稀疏叠加码，其解码复杂度与设计矩阵的大小成线性比例。解码器的性能进行了严格的分析，它是渐近实现AWGN容量与适当的功率分配。仿真结果表明，在有限的块长度的解码器的性能。我们引入了一个功率分配方案，以提高经验性能，并演示了如何解码复杂度可以显着降低使用阿达玛设计矩阵。
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.