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

在该方案中，我们设计了基于穿孔极化码的速率相容码族的构造。为了克服标准结构带来的长度限制，我们探索了三种新的方法，努力寻求最优解，并设计出高效的启发式算法。简化低复杂度的编解码器结构是最重要的设计目标，使其在延迟受限的环境中具有竞争力。该方案构造的码族可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)，在其原始设计中，极性码的可能块长度被限制在极化核下维度的整数次方。因此，更灵活地调整它们的长度并不是一件容易的事。为了构造速率兼容的基于删余极化码的码族，删余模式必须满足一定的嵌套约束，因此有必要开发适应这些额外约束的方法。作为第一步，提出了一种基于删余模式的结构特性的联合优化策略，通过联合优化索引集和删余模式来尝试最优的删余极性码的构造。此外，为了探索基于删截极性码的速率兼容码族构造的有效启发式方法，结合嵌套删余模式的上述约束条件，研究了两种新的删余方法。第一种方法基于极化码生成矩阵的代数分解，而第二种方法采用了有前景的准一致删余技术，两个交叉任务通过改善所得到的码构造的性能来帮助推进这些发现。第一个目标是通过由动态冻结符号给出的附加约束来辅助解码器来增强纠错能力。其次，提出了一种通过整数线性规划来提高指标集选择质量的方法。最后，在已有的继电保护系统理论研究的基础上，提出了一种新的改进方法。由于这些结果假设通过调整码长来实现码率的完美自适应，因此，中继场景为码率兼容的码族提供了最重要的应用领域。作为第二个应用领域，我们研究了在HARQ-IR方案中开发的速率兼容码族的性能。

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.