摘要
The existing cyclic redundancy check(CRC)-aided successive cancellation list(CA-SCL) decoder partitions the decoding process into two steps, where an SCL is followed by a CRC check. An SCL decoder can approach the maximum-likelihood(ML) decoding performance of the inner polar codes using a sufficiently large list; however, in this case, CRC is only used for performing error detection. Therefore, the decoding performance of the outer CRC is different from that of ML because the errors are not rectified, which degrades the performance of the entire concatenated codes. In this study, we propose a sphere decoder(SD) that can achieve the ML performance of polar codes concatenated with CRC to address the suboptimality of CASCL decoding. The proposed SD performs joint decoding of the CRC-polar codes in a single step, thereby avoiding the polar decoding and CRC detection decoding scheme. Because the proposed SD guarantees the ML decoding performance of the CRC-polar concatenated codes, the simulation results demonstrate that the block error rate(BLER) of the proposed SD acts as the lower bound of the CA-SCL decoding performance. Further, a new initial radius selection method is proposed for the SD to reduce the average decoding complexity. The simulations demonstrate that the proposed initial radius selection method reduces more amount of decoding complexity when compared with that reduced using sequential step size methods.
The existing cyclic redundancy check(CRC)-aided successive cancellation list(CA-SCL) decoder partitions the decoding process into two steps, where an SCL is followed by a CRC check. An SCL decoder can approach the maximum-likelihood(ML) decoding performance of the inner polar codes using a sufficiently large list; however, in this case, CRC is only used for performing error detection. Therefore, the decoding performance of the outer CRC is different from that of ML because the errors are not rectified, which degrades the performance of the entire concatenated codes. In this study, we propose a sphere decoder(SD) that can achieve the ML performance of polar codes concatenated with CRC to address the suboptimality of CASCL decoding. The proposed SD performs joint decoding of the CRC-polar codes in a single step, thereby avoiding the polar decoding and CRC detection decoding scheme. Because the proposed SD guarantees the ML decoding performance of the CRC-polar concatenated codes, the simulation results demonstrate that the block error rate(BLER) of the proposed SD acts as the lower bound of the CA-SCL decoding performance. Further, a new initial radius selection method is proposed for the SD to reduce the average decoding complexity. The simulations demonstrate that the proposed initial radius selection method reduces more amount of decoding complexity when compared with that reduced using sequential step size methods.
引文
1 Arikan E.Channel polarization:a method for constructing capacity-achieving codes for symmetric binary-input memoryless channels.IEEE Trans Inform Theor,2009,55:3051-3073
2 Tal I,Vardy A.List decoding of polar codes.IEEE Trans Inform Theor,2015,61:2213-2226
3 Niu K,Chen K.CRC-aided decoding of polar codes.IEEE Commun Lett,2012,16:1668-1671
4 Tahir B,Schwarz S,Rupp M.BER comparison between convolutional,turbo,LDPC,and polar codes.In:Proceedings of the 24th International Conference on Telecommunications(ICT),Limassol,2017.1-7
5 Cao C,Kuang J,Fei Z,et al.Low complexity list successive cancellation decoding of polar codes.IET Commun,2014,8:3145-3149
6 Xu Q Y,Pan Z W,Liu N,et al.A complexity-reduced fast successive cancellation list decoder for polar codes.Sci China Inf Sci,2018,61:022309
7 Ryan W E,Lin S.Channel Codes Classical And Modern.New York:Cambridge University Press Ltd.,2009.110-111
8 Kazakov P.Fast calculation of the number of minimum-weight words of CRC codes.IEEE Trans Inform Theor,2001,47:1190-1195
9 Castagnoli G,Brauer S,Herrmann M.Optimization of cyclic redundancy-check codes with 24 and 32 parity bits.IEEETrans Commun,1993,41:883-892
10 Kahraman S,Celebi M E.Code based efficient maximum-likelihood decoding of short polar codes.In:Proceedings of2012 IEEE International Symposium on Information Theory(ISIT),Cambridge,2012.1967-1971
11 Niu K,Chen K,Lin J.Low-complexity sphere decoding of polar codes based on optimum path metric.IEEE Commun Lett,2014,18:332-335
12 Guo J,Fabregas A G.Efficient sphere decoding of polar codes.In:Proceedings of IEEE International Symposium on Information Theory(ISIT),Hong Kong,2015.236-240
13 Hashemi S A,Condo C,Gross W J.List sphere decoding of polar codes.In:Proceedings of the 49th Asilomar Conference on Signals,Systems and Computers,Pacific Grove,2015.1346-1350
14 Hashemi S A,Condo C,Gross W J.Matrix reordering for efficient list sphere decoding of polar codes.In:Proceedings of 2016 IEEE International Symposium on Circuits and Systems(ISCAS),Montreal,2016.1730-1733
15 Husmann C,Nikolaou P C,Nikitopoulos K.Reduced latency ML polar decoding via multiple sphere-decoding tree searches.IEEE Trans Veh Technol,2018,67:1835-1839
16 Trifonov P.Efficient design and decoding of polar codes.IEEE Trans Commun,2012,60:3221-3227
17 Tal I,Vardy A.How to construct polar codes.IEEE Trans Inform Theor,2013,59:6562-6582
18 He G,Belfiore J C,Land I,et al.Beta-expansion:a theoretical framework for fast and recursive construction of polar codes.In:Proceedings of IEEE Global Communications Conference,Singapore,2017.1-6
19 Koopman P,Chakravarty T.Cyclic redundancy code(CRC)polynomial selection for embedded networks.In:Proceedings of International Conference on Dependable Systems and Networks,Florence,2004.145-154
20 Agrell E,Eriksson T,Vardy A,et al.Closest point search in lattices.IEEE Trans Inform Theor,2002,48:2201-2214
21 Zhang Q,Liu A,Pan X,et al.CRC code design for list decoding of polar codes.IEEE Commun Lett,2017,21:1229-1232
22 Hassibi B,Vikalo H.On the sphere-decoding algorithm I.Expected complexity.IEEE Trans Signal Process,2005,53:2806-2818
23 Zhao W,Giannakis G B.Sphere decoding algorithms with improved radius search.IEEE Trans Commun,2005,53:1104-1109
24 Balatsoukas-Stimming A,Parizi M B,Burg A.LLR-based successive cancellation list decoding of polar codes.IEEETrans Signal Process,2015,63:5165-5179
1)This process is equivalent to using K linearly independent CRC codewords to form the generator matrix.
