Enhancing Iterative Decoding of Polar-like Code Constructions

在过去的60年中，信道编码领域已经从通过奇偶校验位的简单错误检测发展到使用专用代数码或级联编码方案与其各自的(迭代)解码器相结合的强大纠错。这些方案可以非常接近理论容量极限。虽然过去十年的大多数努力都集中在低密度奇偶校验码(LDPC)上，或者最近集中在其空间耦合的后代上，但这项提议是关于研究和加强该领域的另一项重要发展，即由E.Arikan于2008年提出的被称为“极性码”的发展。他证明了在无限长的码字长度下，极性码可以达到任意对称二进制输入离散无记忆信道(BI-DMC)的容量。与具有接近容量性能的其他类似随机的码相比，极性码具有非常规则的(代数)结构，为高效、低复杂性的硬件实现打开了可能性；当考虑到硅芯片技术中的路由开销时，这一点变得特别明显，这可能很容易成为最先进的LDPC码的迭代解码器的禁忌。虽然认识到极性码与Reed-Muller(RM)码密切相关是有启发意义的，但它们的顺序SC译码算法(以及所谓的冻结比特信道的选择)遵循了完全不同的方法，导致了许多吸引人的研究问题。在该方案中，我们试图对极性码的信任传播译码(BP)有一个更全面的理解，以提高有限长度极(和类极)码的误码率性能，并通过为高度并行化的译码实现铺平道路，从而降低译码的计算复杂度和延迟。为此，我们需要设计适合于BP译码的极性码，而不是传统的假设SC译码的方法。此外，改进的分析工具对于更好地理解迭代BP解码器的动力学也是必不可少的，例如“分散的”外部信息传递(EXIT)图或密度演化(DE)图。此外，通过对基本极化码结构的扩展，可以得到在迭代BP译码下具有改善误码性能的新型类极化码。首先，尝试使用基于图的辅助编码的串联/扩充方法或应用空间耦合的概念被证明是有希望的。将BP解码器与类似于连续取消列表解码器的列表概念相结合，以及将改进的BP解码策略与诸如用于在标量和矢量(MIMO)信道上通信的高阶调制的信道接口相结合，补充了对该领域进展的公开研究问题的选择。

Over the past 60 years, the field of channel coding has evolved from simple error detection through parity bit checking to powerful error correction using dedicated algebraic codes or concatenated coding schemes in conjunction with their respective (iterative) decoders. Those schemes can approach the theoretical capacity limits very closely. While most efforts over the past decade have focused on low-density parity-check (LDPC) codes, or, more recently, their spatially coupled offsprings, this proposal is about studying and enhancing another important development in the field, referred to as "polar codes", introduced by E. Arikan in 2008. He proved that polar codes can achieve capacity of any symmetric Binary Input-Discrete Memoryless Channel (BI-DMC) under Successive Cancellation (SC) decoding for infinite codeword length. As opposed to other "random-like" codes with close-to-capacity performance, polar codes have a very regular (algebraic) structure, opening up the potential for efficient low-complexity hardware implementations; this becomes particularly evident when accounting for the routing overhead in silicon chip technology, which may easily become prohibitive for iterative decoders of state-of-the-art LDPC codes. While it is instructive to realize that polar codes are closely related to Reed--Muller (RM) Codes, their sequential SC decoding algorithm (and thus the selection of the, so called, "frozen" bit channels) follow a quite different approach, leading to many attractive research questions. In this proposal, we seek to find a more comprehensive understanding of belief propagation decoding (BP) for polar codes, to enhance the BER performance of finite-length polar (and polar-like) codes, and to reduce computational complexity and latency of decoding by paving the way to highly parallelized decoder implementations. For this, we need to design polar codes tailored to BP decoding, deviating from the traditional approaches that assume SC decoding. Also, improved analysis tools are essential for better understanding the dynamics of the iterative BP decoder, such as "scattered" Extrinsic Information Transfer (EXIT) charts or density evolution (DE). Moreover, by extending the basic polar code structure, it is possible to obtain novel "polar-like" codes with improved BER performance under iterative BP decoding. First attempts using concatenation/augmentation approaches with auxiliary graph-based codes or applying the concept of spatial coupling turned out to be promising. Combining the BP decoder with a list concept, akin to the successive cancellation list decoder, and the combination of improved BP decoding strategies with channel interfaces such as higher-order modulation for communicating over scalar and vector (MIMO) channels, complement the selection of open research questions for progressing the field.