We consider sparse regression codes (SPARCs) over complex AWGN channels. Such codes can be efficiently decoded by an approximate message passing (AMP) decoder, whose performance can be predicted via so-called state evolution in the large-system limit. In this paper, we mainly focus on how to use concatenation of SPARCs and cyclic redundancy check (CRC) codes on the encoding side and use list decoding on the decoding side to improve the finite-length performance of the AMP decoder for SPARCs over complex AWGN channels. Simulation results show that such a concatenated coding scheme works much better than SPARCs with the original AMP decoder and results in a steep waterfall-like behavior in the bit-error rate performance curves. Furthermore, we apply our proposed concatenated coding scheme to spatially coupled SPARCs. Besides that, we also introduce a novel class of design matrices, i.e., matrices that describe the encoding process, based on circulant matrices derived from Frank or from Milewski sequences. This class of design matrices has comparable encoding and decoding computational complexity as well as very close performance with the commonly-used class of design matrices based on discrete Fourier transform (DFT) matrices, but gives us more degrees of freedom when designing SPARCs for various applications.

中文翻译：

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使用列表解码提高稀疏回归码的有限长度性能


我们考虑复杂 AWGN 通道上的稀疏回归码 (SPARC)。此类代码可以通过近似消息传递（AMP）解码器进行有效解码，其性能可以通过大系统极限下的所谓状态演化来预测。在本文中，我们主要关注如何在编码端使用SPARC和循环冗余校验（CRC）码的级联以及在解码端使用列表解码来提高SPARC的AMP解码器相对于复杂AWGN的有限长度性能渠道。仿真结果表明，这种级联编码方案的工作效果比带有原始 AMP 解码器的 SPARC 好得多，并导致误码率性能曲线出现陡峭的瀑布状行为。此外，我们将我们提出的级联编码方案应用于空间耦合的 SPARC。除此之外，我们还引入了一类新颖的设计矩阵，即描述编码过程的矩阵，基于从 Frank 或 Milewski 序列导出的循环矩阵。此类设计矩阵与基于离散傅里叶变换 (DFT) 矩阵的常用设计矩阵类具有相当的编码和解码计算复杂度以及非常接近的性能，但在为各种应用设计 SPARC 时为我们提供了更多的自由度。