Rate-Compatible Codes Based on Punctured Polar Codes for Future Wireless Applications (PACA), funded by DFG (2019-)

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.

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