Enhancing Iterative Decoding of Polar-like Code Constructions

在过去的60年里，信道编码领域已经从通过奇偶校验的简单错误检测发展到使用专用代数码或连接编码方案及其各自（迭代）解码器的强大纠错。这些方案可以非常接近理论容量极限。虽然在过去的十年中，大多数的努力都集中在低密度奇偶校验码（LDPC）上，或者最近，他们的空间耦合的后代，但这个建议是关于研究和加强该领域的另一个重要发展，即E. Arikan在2008年提出的“极性码”。他证明了在无限码字长度的连续对消（SC）译码下，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。与其他具有接近容量性能的“随机”代码相反，极性代码具有非常规则的（代数）结构，为高效的低复杂性硬件实现开辟了潜力；当考虑到硅芯片技术中的路由开销时，这一点变得尤为明显，这可能很容易成为最先进的LDPC代码的迭代解码器的禁忌。虽然认识到极性码与Reed- Muller （RM）码密切相关是有指导意义的，但它们的顺序SC解码算法（以及所谓的“冻结”位通道的选择）遵循完全不同的方法，导致许多有吸引力的研究问题。在本提案中，我们试图找到对极性码的信念传播解码（BP）的更全面的理解，以提高有限长度极性（和类极性）码的误码率性能，并通过为高度并行解码器实现铺平道路来降低解码的计算复杂性和延迟。为此，我们需要设计适合BP解码的极性码，而不是传统的假设SC解码的方法。此外，改进的分析工具对于更好地理解迭代BP解码器的动态是必不可少的，例如“分散的”外在信息传递（EXIT）图表或密度演化（DE）。此外，通过扩展基本的极性码结构，可以在迭代BP解码下获得具有更高误码率性能的新型“类极性”码。第一次尝试使用连接/增强方法和辅助的基于图的代码或应用空间耦合的概念，结果证明是有希望的。将BP解码器与列表概念（类似于连续消列解码器）相结合，并将改进的BP解码策略与信道接口（如用于在标量和矢量（MIMO）信道上通信的高阶调制）相结合，补充了开放研究问题的选择，以推动该领域的发展。

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.