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.
翻译:本文研究对复杂添加式白高斯噪音(AWGN)频道通信的稀少叠加代码( SPARC) 的概括性。 在SPARC 中, 代码簿的定义是设计矩阵, 每个代码词都是通过将设计矩阵乘以稀有信息矢量而生成的。 在标准 SPARC 构造中, 信息是在信息矢量的非零条目位置进行编码的。 在本文中, 信息是在信息矢量的非零条目的位置和非零条目值编码的 SPARC 中进行编码的。 在 SPARC 频道中, 信息是编码的。 我们侧重于非零条目从一个阶段转换键( PSK) 星座中获取数值的情况。 我们提出一个计算高效的近似信息传递解码, 并获得关于预测解码器误差性能的状态演化参数的分析界限。 我们利用这些界限显示, PSK 调整式 SPARC 是在复杂的WGN 频道中实现的模拟性能,, 无论是空间组合式组合式变换式或变力性能到SPLIPLADLADLADL。 我们还可以显示S 的性能的性能。