基于循环冗余校验的极化码研究
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摘要
极化码具有简单明确的编码方式和译码算法,在理论上被证明可以达到香农极限。但是其连续删除译码(SC译码)始终在单路径上逐比特进行译码,导致其实际译码性能并不理想。连续删除列表译码(SCL译码)是SC译码的改进型算法,这种译码方式以付出一定译码复杂度为代价提高了极化码的译码性能。而将SCL译码结合循环冗余校验(CRC)可以译码多路径中错误译码的概率,基于这一点该文将对不同CRC码结合极化码所产生的性能差异进行分析,从而得到合适的CRC
The polar code which has a simple and definite encoding mode and decoding algorithm is proved that it can reach the Shannon limit theoretically,but its successive cancellation decoding(SCD)performs decoding along the single path bit by bit,leading to unsatisfactory practical decoding performance. The successive cancellation list decoding(SCLD)is a modi-fied algorithm of the SCD,which improves the decoding performance of the polar code at the cost of increasing the decoding complexity. The combination of SCLD and the cyclic redundancy check(CRC)can further reduce the probability of decoding er-rors in the multiple paths of the SCLD without increase of the decoding complexity. Based on this,the performance difference generated by different combinations of CRC codes with polar codes is analyzed in this paper,so as to obtain appropriate combi-nations of CRC codes with polar codes.
The polar code which has a simple and definite encoding mode and decoding algorithm is proved that it can reach the Shannon limit theoretically,but its successive cancellation decoding(SCD)performs decoding along the single path bit by bit,leading to unsatisfactory practical decoding performance. The successive cancellation list decoding(SCLD)is a modi-fied algorithm of the SCD,which improves the decoding performance of the polar code at the cost of increasing the decoding complexity. The combination of SCLD and the cyclic redundancy check(CRC)can further reduce the probability of decoding er-rors in the multiple paths of the SCLD without increase of the decoding complexity. Based on this,the performance difference generated by different combinations of CRC codes with polar codes is analyzed in this paper,so as to obtain appropriate combi-nations of CRC codes with polar codes.
引文
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[7]CHEN K,NIU K,LIN J R.A reduced-complexity successive cancellation list decoding of polar codes[C]//Proceedings of77th Vehicular Technology Conference(VTC Spring).Dresden:IEEE,2013:1-5.
[8]FAN Y Z,XIA C Y,CHEN J,et al.A low-latency list successive-cancellation decoding implementation for polar codes[J].IEEE journal on selected areas in communications,2016,34(2):303-317.
[9]ZHANG Q S,LIU A J,PAN X F,et al.CRC code design for list decoding of polar codes[J].IEEE communications letters,2017,21(6):1229-1232.
[10]LI S B,LU L J,DENG Y Q,et al.A reused-public-path successive cancellation list decoding for polar codes with CRC[J].IEEE communications letters,2017,21(12):2566-2569.
[11]MURATA T,OCHIAI H.On design of CRC codes for polar codes with successive cancellation list decoding[C]//Proceedings of IEEE International Symposium on Information Theory.Aachen:IEEE,2017:1-6.
[12]YU Q P,SHI Z P,YAN Q H,et al.Hybrid parity-check and CRC aided SCL decoding for polar codes[C]//Proceedings of IEEE International Conference on Internet of Things(iThings)and IEEE Green Computing and Communications(GreenCom)and IEEE Cyber,Physical and Social Computing(CPSCom)and IEEE Smart Data(SmartData).Chengdu:IEEE,2016:11-15.
[2]XING C,WANG B,ZHAO S M.A reduced-complexity successive-cancellation decoding algorithm for polar codes[C]//Proceedings of 6th International Congress on Image and Signal Processing.Hangzhou:IEEE,2013:5-10.
[3]Tal I,VARDY A.List decoding of polar codes[C]//Proceedings of IEEE International Symposium on Information Theory,St.Petersburg:IEEE,2011:1-11.
[4]CAO M,ZHAO S,ZHAO S M.Multiple CRC-aided variable successive cancellation list decoder of polar codes[J].The journal of China Universities of Posts and Telecommunications,2017,24(2):83-88.
[5]HASHEMI S A,BALATSOUKAS-STIMMING A,GIARD P,et al.Partitioned successive-cancellation list decoding of polar codes[C]//Proceedings of IEEE International Conference on Acoustics,Speech and Signal Processing.Shanghai:IEEE,2015:1-4.
[6]BALATSOUKAS-STIMMING A,PARIZI M B,BURG A.LLR-based successive cancellation list decoding of polar codes[J].IEEE transactions on signal processing,2015,63(19):5165-5179.
[7]CHEN K,NIU K,LIN J R.A reduced-complexity successive cancellation list decoding of polar codes[C]//Proceedings of77th Vehicular Technology Conference(VTC Spring).Dresden:IEEE,2013:1-5.
[8]FAN Y Z,XIA C Y,CHEN J,et al.A low-latency list successive-cancellation decoding implementation for polar codes[J].IEEE journal on selected areas in communications,2016,34(2):303-317.
[9]ZHANG Q S,LIU A J,PAN X F,et al.CRC code design for list decoding of polar codes[J].IEEE communications letters,2017,21(6):1229-1232.
[10]LI S B,LU L J,DENG Y Q,et al.A reused-public-path successive cancellation list decoding for polar codes with CRC[J].IEEE communications letters,2017,21(12):2566-2569.
[11]MURATA T,OCHIAI H.On design of CRC codes for polar codes with successive cancellation list decoding[C]//Proceedings of IEEE International Symposium on Information Theory.Aachen:IEEE,2017:1-6.
[12]YU Q P,SHI Z P,YAN Q H,et al.Hybrid parity-check and CRC aided SCL decoding for polar codes[C]//Proceedings of IEEE International Conference on Internet of Things(iThings)and IEEE Green Computing and Communications(GreenCom)and IEEE Cyber,Physical and Social Computing(CPSCom)and IEEE Smart Data(SmartData).Chengdu:IEEE,2016:11-15.