Rate-Compatible Codes Based on Punctured Polar Codes for Future Wireless Applications

在这个提议中，我们设计了基于穿刺极性码的速率兼容码族结构。为了克服标准结构对长度的限制，我们探索了三种新颖的方法来寻求最优解，并设计了有效的启发式方法。促进低复杂性编码器和解码器结构是最重要的设计目标，在延迟受限的环境中实现具有竞争力的性能。本文构建的码族应用于中继场景，以及具有增量冗余的混合ARQ方案（HARQ-IR方案）。在最初的设计中，极化码可能的块长度被限制为极化核下维数的整数次幂。因此，更灵活地调整它们的长度是非常重要的。一种很有希望的方法是穿刺。为了构建基于穿刺极性码的速率兼容代码族，穿刺模式必须满足某些嵌套约束，因此需要开发方法来适应这些额外的约束。首先，提出了一种基于穿刺模式结构特性的联合优化策略，通过对索引集和穿刺模式的联合优化来尝试穿刺极码的最优构造。在此基础上，探讨了基于穿刺极化码的高效启发式编码方法，研究了两种基于嵌套穿刺模式约束的新型穿刺方法。第一种方法是基于极性码生成器矩阵的代数分解，第二种方法采用了准均匀穿刺技术。两个交叉任务通过改进结果代码结构的性能来帮助推进这些发现。第一个目标是通过通过动态冻结符号给出的附加约束来帮助解码器增强纠错能力。第二章探讨了一种利用整数线性规划提高索引集选择质量的方法。最后，我们在现有继电系统理论研究的基础上进行了进一步的研究。由于这些结果通过调整代码的长度来假设代码速率具有完美的适应性，因此中继场景为最重要的速率兼容代码族提供了应用领域。作为第二个应用领域，我们探讨了在HARQ-IR方案中开发的速率兼容代码族的性能。

In this proposal, we design constructions of rate-compatible families of codes based on puncturing polar codes. To overcome the length restrictions imposed by their standard construction, we explore three novel approaches striving for optimal solutions, as well as devising efficient heuristics.Facilitating a low-complexity encoder and decoder structure is a design goal of paramount interest, enabling competitive performance in latency-constrained environments. Applications for the families of codes constructed in this proposal are found in relay scenarios, as well as hybrid ARQ schemes with incremental redundancy (HARQ-IR schemes).In their original design, possible block lengths of polar codes are limited to integer powers of the dimension underlying polarization kernel. As a result, it is non-trivial to adapt their lengths more flexibly. One promising way to do so is given by puncturing.In order to construct rate-compatible code families based on puncturing polar codes, the puncturing patterns have to satisfy certain nesting constraints, hence necessitating development of methods to accomodate for these additional constraints.As a first step, a joint optimization strategy based on exploiting structural properties of puncturing patterns is proposed, attempting optimal construction of punctured polar codes by jointly optimizing the index set and the puncturing pattern. Furthermore, exploring efficient heurisitcs for the construction of rate-compatible code families based on puncturing polar codes, two novel puncturing approaches are investigated, incorporating the aformentioned constraints of nested puncturing patterns. The first approach is based on algebraic decompositions of the polar code generator matrix, while the second adapts the promising technique of quasi-uniform puncturing.Two intersectional tasks help to advance these findings by improving the performance of the resulting code constructions. The first aims at enhancing error correction capabilities by assisting decoders via additional constraints, given by dynamic frozen symbols. The second explores a technique to improve the quality of the index set selection via integer linear programming.Finally, we build on our existing research in the theory of relaying systems. As these results assume perfect adaptibility of code rates via adapting the length of the codes, relaying scenarios provide application domains for rate-compatible code families of paramount interest. As a second application domain, we explore the performance of the rate-compatible code families developed in HARQ-IR schemes.