Construction of Polar Codes Based on Memetic Algorithm

Abstract

As an emerging coding technique chosen by the 5th generation wireless systems (5G) standardization process, polar coding has attracted the attention of both academia and industry in recent years. The currently used construction methods of polar code are generally based on the reliability of each polarized sub-channel, which directly correspond to the Successive Cancellation (SC) decoding algorithm. However, much less is known about the optimal construction of polar codes under more sophisticated decoding methods such as the Successive Cancellation List (SCL) decoding. There is currently no perfect theory to derive the optimal construction for the SCL decoding to the best of our knowledge, because finding such optimal construction of SCL is considered to be a hard problem for normal choices of the list size. To address this problem, in this paper we turn to evolutionary computation, and propose a memetic algorithm by incorporating prior knowledge obtained from both the channel estimation of the SC-profile and the codeword weight evaluation of the RM-profile, shorted as MA-SCRM. The potential constructions of polar codes are expressed as binary sequences which are processed as the individuals of the population in MA-SCRM. Based on the prior knowledge obtained from the SC-profile and the Reed-Muller-profile, we design special initialization and evolutional operators for polar codes construction. An elitism archive is also introduced to maintain promising constructions and accelerate the convergence of the algorithm. For the SCL decoding, MA-SCRM obtains polar-coding constructions that are more excellent than the SC decoder construction in the sense of block error probability. Compared with the SC decoding construction method, MA-SCRM can reduce the block error probability by up to 48.78% for the original block error rate around <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{-2}$</tex-math></inline-formula> , and more improvement can be observed for lower original block error rate.