Sparse regression codes (SPARC) connect the sparse signal recovery framework of compressive sensing with error control coding techniques. SPARC encoding produces codewords which are \emph{sparse} linear combinations of columns of a dictionary matrix. SPARC decoding is accomplished using sparse signal recovery algorithms. We construct dictionary matrices using Gold codes and mutually unbiased bases and develop suitable generalizations of SPARC (GSPARC). We develop a greedy decoder, referred as match and decode (MAD) algorithm and provide its analytical noiseless recovery guarantees. We propose a parallel greedy search technique, referred as parallel MAD (PMAD), to improve the performance. We describe the applicability of GSPARC with PMAD decoder for multi-user channels, providing a non-orthogonal multiple access scheme. We present numerical results comparing the block error rate (BLER) performance of the proposed algorithms for GSPARC in AWGN channels, in the short block length regime. The PMAD decoder gives better BLER than the approximate message passing decoder for SPARC. GSPARC with PMAD gives comparable and competitive BLER performance, when compared to other existing codes. In multi-user channels, GSPARC with PMAD decoder outperforms the sphere packing lower bounds of an orthogonal multiple access scheme, which has the same spectral efficiency.
翻译:稀疏回归码(SPARC)将压缩感知的稀疏信号恢复框架与错误控制编码技术相连接。 SPARC编码生成的码字是字典矩阵列的稀疏线性组合。 SPARC解码使用稀疏信号恢复算法完成。我们使用Gold码和互补基构造字典矩阵,并开发适当的SPARC的推广(GSPARC)。我们开发了一种贪婪解码器,称为匹配和解码(MAD)算法,并提供其在无噪声恢复中的分析保证。我们提出了一种并行的贪婪搜索技术,称为并行MAD(PMAD),以提高性能。我们描述了GSPARC与PMAD解码器在多用户信道中的适用性,提供一种非正交多址(MAO)方案。我们在短块长度范围内,提供了使用GSPARC的算法在AWGN信道中的块错误率(BLER)性能的数字结果。 PMAD解码器比用于SPARC的近似消息传递解码器具有更好的BLER。与其他现有代码相比,使用PMAD的GSPARC提供了可比和具有竞争力的BLER性能。在多用户信道中,使用PMAD解码器的GSPARC胜过具有相同频谱效率的正交多址方案的球形包装下限。