Research On Algorithms Of Encoding And Decoding For Polar Codes

Scholars have proposed lots of coding theories and constructed many goodperformance encoding and decoding schemes after years of development in thefield of error control coding, but all these schemes haven’t achieved the channelcapacity in theory.While, polar codes achieve the capacity of symmetric channelsin theory,and with the growth of the code length, frame error rate decaysexponentially, The good news is that the cost of encoding and decoding of polarcodes is linear complexity,which makes it possible to produce good performancecodes.Since the polar code is born recently, the performance of encoding anddecoding schemes at short to moderate block lengths is disappointing,Arikan,who discovered the polar codes, didn’t give the encoding scheme withlow complexity under channels except the binary erasure channel(BEC), on theother hand, the performance of traditional SC decoder is not very good. Thesetwo aspects limit the use of polar codes.We will start with these two aspects andstudy the encoding scheme and several decoding schemes at short to moderateblock lengths of polar codes under the additive white Gaussian noisechannel(AWGNC). By Simulation,we analyse the performance of all theseschemes.At first,we puts forward a model from the AWGNC to BEC, and select thechannels under BEC, and then we provide a fast selection algorithm and somerobust conclusions.Then, we analyse the channel selection problems underAWGNC based on channel weakening and strengthening operations,and wecomplete the implementation of the scheme.Based on the iterative formulas given by Arikan,we complete the decoderunder matlab,and solve the problem of computational accuracy.We analyse theSC list (SCL) decoder evolved from the SC decoder, then we analyse theCRC-Aided SCL decoder. Two BCH-Aided SC decoders and one RS-Aided SCdecoder are given to improve the decoding performance of polar codes.