Novel Multi-Parameter based Rate-Matching of Polar Codes

Polar codes have garnered a lot of attention from the scientific community owing to their low-complexity implementation and provably capacity achieving capability. They have been proposed to be used in 5G networks. However, the conventional approach of channel polarization introduced by Arikan in [1], can be used to design only codewords of length N = 2ⁿ, which is a major limitation when codewords of length N ≠ 2ⁿ are required. To perform rate-matching for such codeword lengths, using non-2×2 circuit kernels or resizing techniques (upsizing or downsizing) are the solutions. As per the technical specifications of 3GPP 5G NR standardization document [2], a unique threshold coderate value is used to determine whether puncturing or shortening should be used for downsizing polar codes, which although being plausibly optimal for the system configurations in [2], might be sub-optimal over a wider range of design parameter settings. In this paper, we introduce a novel downsizing type-selection (DTS) parameter which takes into account codeword length, coderate, effect of polarization and number of downsized bits, to determine the preferable method for downsizing polar codes.