Research Of Decoding Schemes For Polar Codes

Polar codes,proposed by Arikan in 2009,are one kind of error correcting codes.By channel combining and channel splitting,polar codes realize channel polarization.One part of polarized channels are almost perfect channels with no noise.The other part of polarized channels are useless channels without the ability of transmitting signals.As the length of codes approaching infinity,the ratio of perfect channels to the total number of polarized channels approaches the transmission rate.Therefore,Polar codes are the first class of codes that provably achieve the capacity of any symmetric binary-input discrete memoryless channel(BDMC)with efficient encoding and decoding algorithms based on channel polarization.Owning to such ability,polar codes have been adopted for the enhanced mobile broadband control channel of the fifth generation(5G)wireless communications standard.In this paper,the decoding schemes are considered as the main research field.Successive cancellation decoding,Belief Propagation decoding and machine learning based decoding algorithms are the main decoding schemes for polar codes.Based on existing research progress,there are four problems for this paper to solve:(1)Traditional successive cancellation decoding scheme can not adjust the list length according to the actual situations.For this problem,we propose successive cancellation list decoder with adaptive list length.The proposed algorithm can adjust the list length with the difficulty of decoding procedure.When the decoding procedure is relatively simple,the list length is reduced to save computational resources.On the other hand,when the decoding process becomes complicated,the list length is increased to make sure the decoder can decode correctly.As a result,the proposed algorithm can modify the average list length according to the signal-to-ratio changes.Experimental results prove that it can decrease frame error rate with no computational complexity increased.(2)Based on the permuted facot graph of belief propagation decoder.We propose the concept of sub-graph of permuted factor graph.This brand new concept can offer much more permutation schemes compared with the original one.We prove the permuted factor graph is a subset of the proposed sub-graph of permuted factor graph.Moreover,we propose a new decoder based on the proposed sub-graph of permuted factor graph.The results show that the proposed algorithm can improve frame error rate performance effectively with no computational burden.(3)Traditional machine learning based decoding algorithms does not take the frame error rate of polarized channels into consideration.For this problem,we propose to improve the loss function of machin learning decoders.For the bits with high frame error rate,their contribution to the whole loss values should be less than that with low frame error rate.In this way,the decoder based on neural networks becomes more interpretable than the conventional decoders.The simulation results show that frame error rate performance of the proposed algorithm is slightly better than the na(?)ve neural network decoder.(4)We propose a novel decoding structure which is based on sequence to sequence structure of recurrent neural network.The structure and property of ecurrent neural network is similar to the successive cancellation decoder.Thus,the decoder based on recurrent neural network can learn the actual decoding process rather than only remember the inputs and outputs of polar codes.