Construction of Multi-Kernel Polar Codes With Kernel Substitution

Abstract

Traditional polar codes are constructed based on a size-2 kernel and the code length is thus restricted to an integer power of 2. To achieve flexible code lengths, punctured and shortened schemes are used in the existing 5G standard. Recently, an alternative approach for flexible code lengths, multi-kernel (MK) polar code, has been proposed, which is constructed based on both size-2 and other larges kernels. However, the error-correction performance is not as good as that of the punctured and shortened schemes. In this letter, an MK polar code construction method based on a kernel substitution scheme is proposed, which is a practical scheme to construct the codes using two types of large kernels with the same size so that the error-correction performance can be improved. Compared with the existing MK polar codes, simulation results show that 0.15 - 0.25 dB performance gain can be achieved by SC decoding for most code settings at a block error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> without complexity overhead.