We consider sparse superposition 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.
翻译:我们考虑对复杂的AWGN 频道采用稀少的叠加码码(SPRCs),这种编码可以用大致的信息传递(AMP)解码器有效解码,其性能可以通过大型系统极限的所谓状态演进预测出来。在本文中,我们主要侧重于如何在编码侧使用SPRC的聚合码和循环冗余检查(CRC)代码,并在解码侧使用解码列表解码,以提高 SPARCs AMP 解码器在复杂的AWGN 频道的有限性能。模拟结果显示,这种配对的编码方案比SPARCs在最初的AMP解码器的最初状态演进中预测出来的效果要好得多。此外,我们把我们提议的组合编码编码办法应用于在编码侧向空间连接的SPARCs。 此外,我们还引入了新型的设计矩阵,即描述编码过程的矩阵,它基于从Frank或Millewski 序列中提取的螺旋矩阵,在位标定S-rex-dal Exlicommission mission 时,这一类设计模型可以比较地转换为S-delviewDF 。