论文标题
调制复杂AWGN通道的稀疏叠加代码
Modulated Sparse Superposition Codes for the Complex AWGN Channel
论文作者
论文摘要
本文研究了稀疏叠加代码（SPARC）在复杂的添加剂白色高斯噪声（AWGN）通道上进行通信的概括。在SPARC中，代码簿是根据设计矩阵定义的，并且每个代码字是通过将设计矩阵与稀疏消息向量相乘的生成的。在标准的SPARC构造中，信息在消息向量的非零条目的位置进行了编码。在本文中，我们概括了构造并考虑调制的SPARC，其中信息在消息向量的非零条目的位置和值中编码。我们专注于非零条目从相移键（PSK）星座中取值的情况。我们提出了一个计算有效的近似消息传递（AMP）解码器，并在状态演化参数上获得分析界限，以预测解码器的误差性能。使用这些边界，我们表明，PSK调制的SPARC具有渐近AWGN通道的渐近能力，并具有空间耦合或功率分配。我们还提供数值模拟结果，以证明有限代码长度的错误性能。这些结果表明，向SPARC设计引入调制可以显着降低解码复杂性而无需牺牲误差性能。
This paper studies a generalization of sparse superposition codes (SPARCs) for communication over the complex additive white Gaussian noise (AWGN) channel. In a SPARC, the codebook is defined in terms of a design matrix, and each codeword is a generated by multiplying the design matrix with a sparse message vector. In the standard SPARC construction, information is encoded in the locations of the non-zero entries of the message vector. In this paper we generalize the construction and consider modulated SPARCs, where information in encoded in both the locations and the values of the non-zero entries of the message vector. We focus on the case where the non-zero entries take values from a phase-shift keying (PSK) constellation. We propose a computationally efficient approximate message passing (AMP) decoder, and obtain analytical bounds on the state evolution parameters which predict the error performance of the decoder. Using these bounds we show that PSK-modulated SPARCs are asymptotically capacity achieving for the complex AWGN channel, with either spatial coupling or power allocation. We also provide numerical simulation results to demonstrate the error performance at finite code lengths. These results show that introducing modulation to the SPARC design can significantly reduce decoding complexity without sacrificing error performance.
