Research Of Belief Propagation Decoding Algorithm Of Polar Codes

With the development of channel encoding technology,scholars have developed encoding theories and produced various decoding schemes.In the channel encoding technology,the polar codes proposed by E.Arikan stand out.In the binary discrete memoryless channel,it is strictly proved to be able to reach the Shannon limit in theory and the complexity of encoding and decoding is relatively low.In November2016,3GPP,the international organization for mobile communication standardization,selected polar codes as the encoding scheme of control channel in 5G.Due to the advantages of various practical types of polar codes,it has been widely studied by scholars at home and abroad.Traditional decoding algorithms for polar codes include Successive Cancellation(SC)and Belief Propagation(BP)decoding algorithms,under additive white Gaussian noise(AWGN),BP algorithm is superior to SC algorithm.However,the performance of SC algorithm is not ideal under the condition of medium and short code lengths,so a better decoding method is SC list(SCL)algorithm.But with the increase of list L,the complexity of SCL decoding algorithm will become larger and the parallelism of SCL algorithm itself leads to the low efficiency in decoding.Because BP decoding itself can be implemented in parallel,the research on BP decoding algorithm of polar codes has become the key at present.The basis of BP algorithm is based on factor graph.In this paper,we find that because of the permutability of BP factor graph,these bit channels have changed,which lead to the multi-factor graphs decoding method.The existing theory is not enough to explain the permutability of BP factor graph.Starting from the encoding of polar codes,this paper proves theoretically that the encoding matrix can be decomposed into the product of submatrixs and the position of submatrix can be interchanged arbitrarily,resulting in different encoding graphs.The BP factor graphs correspond to the encoding graphs one by one,thus proving the permutability of the BP factor graph and proposing the principle of selecting the BP factor graph.In orderto reduce the complexity of the existing decoding methods of BP multi-factor graphs,a parallel decoding method of two BP factor graphs is proposed based on the principle proposed in this paper.Simulation results show that,compared with the original BP decoding,the decoding method proposed in this paper has better error performance and lower average number of iterations.Compared with the existing decoding methods of BP multi-factor graphs,when the total number of iterations is fixed at 60,the error performance is basically the same,but the average number of iterations is lower.