Versatile Polar Codes with different Kernel Sizes and Rate Matching approaches

Polar codes, which have been recently proposed as a family of linear block codes, has garnered a lot of attention from the scientific community owing to their low-complexity implementation and provably capacity achieving capability. Thus, they have been proposed to be used for encoding information on the control channels in the upcoming 5G networks. The basic approach introduced by Arikan in [1], to polarize 2 channels of equal capacities to 2 channels of unequal capacities, can be used to design only codewords of length N = 2
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, which might not be desired for the underlying system. Designing polar codes of codeword lengths of the form N ≠ 2
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would broaden their utilitarian aspects and make them adaptable to a wider range of applications. In this paper, we investigate the comparative performance of resized polar codes generated by different techniques and determine the optimal one based on code rate requirements.