A Parallel Decoding Algorithm for Short Polar Codes Based on Error Checking and Correcting
We propose a parallel decoding algorithm based on error checking and correcting to improve the performance of the short polar codes. In order to enhance the error-correcting capacity of the decoding algorithm, we first derive the error-checking equations generated on the basis of the frozen nodes, a...
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| Veröffentlicht in: | TheScientificWorld Jg. 2014; H. 2014; S. 1 - 14 |
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Cairo, Egypt
Hindawi Publishing Corporation
01.01.2014
John Wiley & Sons, Inc Wiley |
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| ISSN: | 2356-6140, 1537-744X, 1537-744X |
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| Abstract | We propose a parallel decoding algorithm based on error checking and correcting to improve the performance of the short polar codes. In order to enhance the error-correcting capacity of the decoding algorithm, we first derive the error-checking equations generated on the basis of the frozen nodes, and then we introduce the method to check the errors in the input nodes of the decoder by the solutions of these equations. In order to further correct those checked errors, we adopt the method of modifying the probability messages of the error nodes with constant values according to the maximization principle. Due to the existence of multiple solutions of the error-checking equations, we formulate a CRC-aided optimization problem of finding the optimal solution with three different target functions, so as to improve the accuracy of error checking. Besides, in order to increase the throughput of decoding, we use a parallel method based on the decoding tree to calculate probability messages of all the nodes in the decoder. Numerical results show that the proposed decoding algorithm achieves better performance than that of some existing decoding algorithms with the same code length. |
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| AbstractList | We propose a parallel decoding algorithm based on error checking and correcting to improve the performance of the short polar codes. In order to enhance the error-correcting capacity of the decoding algorithm, we first derive the error-checking equations generated on the basis of the frozen nodes, and then we introduce the method to check the errors in the input nodes of the decoder by the solutions of these equations. In order to further correct those checked errors, we adopt the method of modifying the probability messages of the error nodes with constant values according to the maximization principle. Due to the existence of multiple solutions of the error-checking equations, we formulate a CRC-aided optimization problem of finding the optimal solution with three different target functions, so as to improve the accuracy of error checking. Besides, in order to increase the throughput of decoding, we use a parallel method based on the decoding tree to calculate probability messages of all the nodes in the decoder. Numerical results show that the proposed decoding algorithm achieves better performance than that of some existing decoding algorithms with the same code length. We propose a parallel decoding algorithm based on error checking and correcting to improve the performance of the short polar codes. In order to enhance the error-correcting capacity of the decoding algorithm, we first derive the error-checking equations generated on the basis of the frozen nodes, and then we introduce the method to check the errors in the input nodes of the decoder by the solutions of these equations. In order to further correct those checked errors, we adopt the method of modifying the probability messages of the error nodes with constant values according to the maximization principle. Due to the existence of multiple solutions of the error-checking equations , we formulate a CRC-aided optimization problem of finding the optimal solution with three different target functions, so as to improve the accuracy of error checking. Besides, in order to increase the throughput of decoding, we use a parallel method based on the decoding tree to calculate probability messages of all the nodes in the decoder. Numerical results show that the proposed decoding algorithm achieves better performance than that of some existing decoding algorithms with the same code length. We propose a parallel decoding algorithm based on error checking and correcting to improve the performance of the short polar codes. In order to enhance the error-correcting capacity of the decoding algorithm, we first derive the error-checking equations generated on the basis of the frozen nodes, and then we introduce the method to check the errors in the input nodes of the decoder by the solutions of these equations. In order to further correct those checked errors, we adopt the method of modifying the probability messages of the error nodes with constant values according to the maximization principle. Due to the existence of multiple solutions of the error-checking equations, we formulate a CRC-aided optimization problem of finding the optimal solution with three different target functions, so as to improve the accuracy of error checking. Besides, in order to increase the throughput of decoding, we use a parallel method based on the decoding tree to calculate probability messages of all the nodes in the decoder. Numerical results show that the proposed decoding algorithm achieves better performance than that of some existing decoding algorithms with the same code length.We propose a parallel decoding algorithm based on error checking and correcting to improve the performance of the short polar codes. In order to enhance the error-correcting capacity of the decoding algorithm, we first derive the error-checking equations generated on the basis of the frozen nodes, and then we introduce the method to check the errors in the input nodes of the decoder by the solutions of these equations. In order to further correct those checked errors, we adopt the method of modifying the probability messages of the error nodes with constant values according to the maximization principle. Due to the existence of multiple solutions of the error-checking equations, we formulate a CRC-aided optimization problem of finding the optimal solution with three different target functions, so as to improve the accuracy of error checking. Besides, in order to increase the throughput of decoding, we use a parallel method based on the decoding tree to calculate probability messages of all the nodes in the decoder. Numerical results show that the proposed decoding algorithm achieves better performance than that of some existing decoding algorithms with the same code length. |
| Audience | Academic |
| Author | Ye, Zhan Pan, Xiaofei Gong, Chao Pan, Kegang Zhang, Yingxian |
| AuthorAffiliation | Laboratory of Satellite Communications, College of Communications Engineering, PLA University of Science and Technology, Nanjing 210007, China |
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| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/25540813$$D View this record in MEDLINE/PubMed |
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| Cites_doi | 10.1109/LCOMM.2011.101811.111480 10.1109/TIT.2009.2021379 10.1109/LCOMM.2012.090312.121501 10.1109/LCOMM.2008.080017 10.1109/TCOMM.2013.070213.120789 10.1109/LCOMM.2013.021213.121633 10.1109/LCOMM.2011.061611.110862 10.1109/TIT.1962.1057683 10.1109/TIT.2010.2080990 10.1109/TCOMM.2013.012313.110692 10.1109/JSAC.2014.140514 |
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| Copyright | Copyright © 2014 Yingxian Zhang et al. COPYRIGHT 2014 John Wiley & Sons, Inc. Copyright © 2014 Yingxian Zhang et al. Yingxian Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Copyright © 2014 Yingxian Zhang et al. 2014 |
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| References_xml | – reference: Divsalar D. Jones C. CTH08-4: protograph LDPC codes with node degrees at least 3 Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM '06) December 2006 San Francisco, Calif, USA 1 5 10.1109/GLOCOM.2006.78 2-s2.0-50949122889 – volume: 55 start-page: 3051 issue: 7 year: 2009 end-page: 3073 ident: 1 article-title: Channel polarization: a method for constructing capacity-achieving codes for symmetric binary-input memoryless channels – ident: 11 article-title: A fast software polar decoder – ident: 5 article-title: List decoding of polar codes – reference: Goela N. Korada S. B. Gastpar M. On LP decoding of polar codes Proceedings of the IEEE Information Theory Workshop (ITW '10) September 2010 Dublin, Ireland 1 5 10.1109/CIG.2010.5592698 2-s2.0-80051938098 – volume: 61 start-page: 3100 issue: 8 year: 2013 end-page: 3107 ident: 6 article-title: Improved successive cancellation decoding of polar codes – reference: Arikan E. Kim H. Markarian G. Özür U. Poyraz E. Performance of short polar codes under ML decoding Proceedings of the ICT-Mobile Summit Conference June 2009 – volume: 16 start-page: 1668 issue: 10 year: 2012 end-page: 1671 ident: 7 article-title: CRC-aided decoding of polar codes – reference: Tal I. Vardy A. List decoding of polar codes Proceedings of the IEEE International Symposium on Information Theory Proceedings (ISIT '11) August 2011 St. Petersburg, Russia 1 5 10.1109/ISIT.2011.6033904 2-s2.0-80054823729 – reference: Massey J. L. Catastrophic error-propagation in convolutional codes Proceedings of the 11th Midwest Symposium on Circuit Theory January 1968 583 587 – volume: 15 start-page: 1378 issue: 12 year: 2011 end-page: 1380 ident: 8 article-title: A simplified successive-cancellation decoder for polar codes – volume: 8 start-page: 21 year: 1962 end-page: 28 ident: 22 article-title: Low-density parity-check codes – volume: 17 start-page: 725 issue: 4 year: 2013 end-page: 728 ident: 9 article-title: Increasing the throughput of polar decoders – volume: 15 start-page: 860 issue: 8 year: 2011 end-page: 862 ident: 20 article-title: Systematic polar coding – reference: Kahraman S. Çelebi M. E. Code based efficient maximum-likelihood decoding of short polar codes Proceedings of the IEEE International Symposium on Information Theory (ISIT '12) July 2012 Cambridge, Mass, USA 1967 1971 10.1109/ISIT.2012.6283643 2-s2.0-84867565147 – reference: Hussami N. Korada S. B. Urbanke R. Performance of polar codes for channel and source coding Proceedings of the IEEE International Symposium on Information Theory (ISIT '09) July 2009 1488 1492 10.1109/ISIT.2009.5205860 2-s2.0-70449484484 – volume: 56 start-page: 6253 issue: 12 year: 2010 end-page: 6264 ident: 3 article-title: Polar codes: characterization of exponent, bounds, and constructions – volume: 32 start-page: 946 issue: 5 year: 2014 end-page: 957 ident: 10 article-title: Fast polar decoders: algorithm and implementation – reference: Arikan E. Polar codes: a pipelined implementation Proceedings of the 4th International Symposium on Broadband Communication (ISBC '10) July 2010 11 14 – reference: Eslami A. Pishro-Nik H. On bit error rate performance of polar codes in finite regime Proceedings of the 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton '10) October 2010 188 194 10.1109/ALLERTON.2010.5706906 2-s2.0-79952418090 – volume: 12 start-page: 447 issue: 6 year: 2008 end-page: 449 ident: 15 article-title: A performance comparison of polar codes and reed-muller codes – reference: Arikan E. Telatar E. On the rate of channel polarization Proceedings of the IEEE International Symposium on Information Theory (ISIT '09) June-July 2009 1493 1495 10.1109/ISIT.2009.5205856 2-s2.0-70449478491 – volume: 61 start-page: 919 issue: 3 year: 2013 end-page: 929 ident: 19 article-title: On finite-length performance of polar codes: stopping sets, error floor, and concatenated design – ident: 8 doi: 10.1109/LCOMM.2011.101811.111480 – ident: 5 – ident: 1 doi: 10.1109/TIT.2009.2021379 – ident: 7 doi: 10.1109/LCOMM.2012.090312.121501 – ident: 11 – ident: 15 doi: 10.1109/LCOMM.2008.080017 – ident: 6 doi: 10.1109/TCOMM.2013.070213.120789 – ident: 9 doi: 10.1109/LCOMM.2013.021213.121633 – ident: 20 doi: 10.1109/LCOMM.2011.061611.110862 – volume: 8 start-page: 21 year: 1962 ident: 22 publication-title: IEEE Transactions on Information Theory doi: 10.1109/TIT.1962.1057683 – ident: 3 doi: 10.1109/TIT.2010.2080990 – ident: 19 doi: 10.1109/TCOMM.2013.012313.110692 – ident: 10 doi: 10.1109/JSAC.2014.140514 |
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| SubjectTerms | Algorithms Binary system Codes Error-correcting codes Graph representations Linear programming Low density parity check codes Models, Theoretical Satellite communications |
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| Title | A Parallel Decoding Algorithm for Short Polar Codes Based on Error Checking and Correcting |
| URI | https://search.emarefa.net/detail/BIM-1051497 https://dx.doi.org/10.1155/2014/895782 https://www.ncbi.nlm.nih.gov/pubmed/25540813 https://www.proquest.com/docview/1552844845 https://www.proquest.com/docview/1641018010 https://pubmed.ncbi.nlm.nih.gov/PMC4142331 https://doaj.org/article/200f3c3a4769448ba1562ada3148e541 |
| Volume | 2014 |
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