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arXiv · 1612.01352

Rate-Compatible Punctured Polar Codes: Optimal Construction Based on Polar Spectra

Kai Niu·Jincheng Dai·Kai Chen·Jiaru Lin·Q. T. Zhang·Athanasios V. Vasilakos
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Abstract

Polar codes are the first class of constructive channel codes achieving the symmetric capacity of the binary-input discrete memoryless channels. But the corresponding code length is limited to the power of two. In this paper, we establish a systematic framework to design the rate-compatible punctured polar (RCPP) codes with arbitrary code length. A new theoretic tool, called polar spectra, is proposed to count the number of paths on the code tree with the same number of zeros or ones respectively. Furthermore, a spectrum distance SD0 (SD1) and a joint spectrum distance (JSD) are presented as performance criteria to optimize the puncturing tables. For the capacity-zero puncturing mode (punctured bits are unknown to the decoder), we propose a quasi-uniform puncturing algorithm, analyze the number of equivalent puncturings and prove that this scheme can maximize SD1 and JSD. Similarly, for the capacity-one mode (punctured bits are known to the decoder), we also devise a reversal quasi-uniform puncturing scheme and prove that it has the maximum SD0 and JSD. Both schemes have a universal puncturing table without any exhausted search. These optimal RCPP codes outperform the performance of turbo codes in LTE wireless communication systems.

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Kai Niu, Jincheng Dai, Kai Chen, Jiaru Lin, Q. T. Zhang, Athanasios V. Vasilakos. 2016-12-05. Rate-Compatible Punctured Polar Codes: Optimal Construction Based on Polar Spectra. https://arxiv.org/abs/1612.01352

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