Research On Improvement Of Check-aided Decoding Algorithms For Polar Codes

Polar codes have developed for more than 20 years since they were invented.Although polar codes have the advantage of achieving channel capacity in theory,the performance of finite-length polar codes is not satisfactory.Decoding algortihms are always the focus of researches of polar codes,especially the improved algorithms based on the Successive Cancellation(SC)algorithm,including Successive Cancellation List(SCL)algorithm,Parity Check(PC)aided SCL algorithm,Cyclic Redundancy Check(CRC)aided SCL algorithm,etc.Based on the SCL algorithm,in order to enhance the performance and reduce the computation complexity,this thesis proposes four improved SCL decoding algorithms.The main contributions are as follows:(1)Targeting at the problem that the PC aided SCL algorithm cannot detect error patterns with even number of error bits,this thesis uses the method of assigning weight for every bit alternatively and proposes an improved decoding algorithm called Alternatively Weighted Parity Check(AWPC)aided SCL algorithm.The AWPC uses one check bit in its encoding,and it can detect 50% error patterns with even number of error bits and 50% error patterns with odd number of error bits.Since the proportion of paths having even number of error bits is much bigger than that of paths having odd number of error bits in the SCL algorithm,the ability of AWPC to detect error paths in decoding is enhanced,and thereby the error performance is improved.(2)In order to find out more error paths,based on the AWPC aided SCL algorithm and using modulo 4 addition,this thesis proposes an improved decoding algorithm called Modulo 4 Sum Check(M4SC)aided SCL algorithm.This algorithm can detect 50% error patterns with even number of error bits and all error patterns with odd number of error bits,which futher improves the error performance.(3)Moreover,by combining modulo 3 addition and modulo 2 addition,this thesis also proposes an improved decoding algorithm called Double Modulo Sum Check(DMSC)aided SCL algorithm.This algorithm can detect 2/3 error patterns with even number of error bits and all error patterns with odd number of error bits.Comared with the M4 SC aided SCL algorithm,DMSC improves the error performance without increasing the computation complexity apparently.(4)Aimming at the problem that the Adaptive CA-SCL algorithm has too much meaningless computation,this thesis proposes an improved decoding algorithm called Adaptive SCL by Backing to the Begining.The new algorithm uses the DMSC coding as mentioned above in precoding to assist decoding by checking the code sequence in every check section.By this means,error detecting can be carried out in time as soon as decoding of one check section is acomplished.Then according to the checking results,the new algorithm will decide if corresponding adaptive strategies are adopted or not,which avoids a lot of useless computation.Compared with the Adaptive CA-SCL algorithm,the Adaptive SCL algorithm by Backing to the Beginning not only reduces the computation complexity,but also improves the error performance.