PA码的迭代译码研究
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摘要
在信道编码理论发展的50多年中,人们一直在寻找Shannon信道编码定理中提出的“好码”。本文在分析了信道编解码理论的基础之上,介绍了由Jing Li提出的乘积累加码(PA码)码,并具体分析了该码的译码结构与和积译码算法。最后用EXIT图对PA码的迭代性能进行了研究,并与仿真结果进行了对比。
本文的内容主要分以下向个部分：
1.介绍了信道编解码基础理论,主要包括信道编解码模型、线性分组码和卷积码的概念、Tanner图与和积算法以及用士兵计数模型理解消息传递算法等。
2.分析了基于单奇偶校验码的Turbo乘积码(TPC/SPC)码,然后给出了PA的编码结构。在此基础之上,研究并给出了PA码的迭代译码结构,并用和积算法对此结构的性能进行了仿真,以验证迭代译码结构的可行性。
3.由于PA码译码涉及到内迭代和外迭代两种迭代,确定迭代次数对性能的影响是PA码工程化的关键问题。本文用EXIT图方法对PA码的迭代次数问题进行了计算和研究,并用计算结果与仿真结果进行了比较。
During the development of the channel coding theory about 50 years, people have been looking for "good codes" defined by Shannon's theory. Based on the analysis of the channel coding theory, Jing Li's Product Accumulate Codes (PA codes) is introduced and then its decoding structure and sum-product decoding algorithm are particularly analyzed. Finnally, EXIT chart is used to study the PA code's iterative decoding performance. The results of the EXIT chart are compared with simulation data. The main work and achievements are shown as follows:
1. This paper introduces basic theories of channel coding, including the channel coding model, the definition of linear grouping code and convolutional code, Tanner chart, sum-product decoding algorithm and the soldier counting model for comprehension of message-passing algorithm.
2. This paper analyzes turbo product code based on single parity check code (TPC/SPC code), and brings in the PA code's coding structure. Then the PA code's iterative decoding structure is studied and presented, and according to the iterative decoding structure, sum-product algorithm is simulated for the purpose of demonstrating the validity of the decoding structure.
3. Two kinds of iterations are concerned in the PA code's iterative decoding structure, so confirming the relationship between iterative numbers and iterative decoding performance is the key to the PA code's engineering achievement. EXIT chart is brought in to study and analyze the iterative numbers and the results are compared with simulation data.
本文的内容主要分以下向个部分：
1.介绍了信道编解码基础理论,主要包括信道编解码模型、线性分组码和卷积码的概念、Tanner图与和积算法以及用士兵计数模型理解消息传递算法等。
2.分析了基于单奇偶校验码的Turbo乘积码(TPC/SPC)码,然后给出了PA的编码结构。在此基础之上,研究并给出了PA码的迭代译码结构,并用和积算法对此结构的性能进行了仿真,以验证迭代译码结构的可行性。
3.由于PA码译码涉及到内迭代和外迭代两种迭代,确定迭代次数对性能的影响是PA码工程化的关键问题。本文用EXIT图方法对PA码的迭代次数问题进行了计算和研究,并用计算结果与仿真结果进行了比较。
During the development of the channel coding theory about 50 years, people have been looking for "good codes" defined by Shannon's theory. Based on the analysis of the channel coding theory, Jing Li's Product Accumulate Codes (PA codes) is introduced and then its decoding structure and sum-product decoding algorithm are particularly analyzed. Finnally, EXIT chart is used to study the PA code's iterative decoding performance. The results of the EXIT chart are compared with simulation data. The main work and achievements are shown as follows:
1. This paper introduces basic theories of channel coding, including the channel coding model, the definition of linear grouping code and convolutional code, Tanner chart, sum-product decoding algorithm and the soldier counting model for comprehension of message-passing algorithm.
2. This paper analyzes turbo product code based on single parity check code (TPC/SPC code), and brings in the PA code's coding structure. Then the PA code's iterative decoding structure is studied and presented, and according to the iterative decoding structure, sum-product algorithm is simulated for the purpose of demonstrating the validity of the decoding structure.
3. Two kinds of iterations are concerned in the PA code's iterative decoding structure, so confirming the relationship between iterative numbers and iterative decoding performance is the key to the PA code's engineering achievement. EXIT chart is brought in to study and analyze the iterative numbers and the results are compared with simulation data.
引文
[1]C. E. Shannon. A mathematical theory of communication. Bell Syst. Tech. J., vol. 27, July-Oct.1948:379～423,623～656.
[2]R. G Gallager. Low-density parity-check codes. IRE Trans. Inform. Theory, Jan. 1962:21-28.
[3]R. M. Tanner. A recursive approach to low complexity codes. IEEE Trans. Inform. Theory, vol. IT-27, Sept.1981:533～547.
[4]D.J.C.MacKay, R.M.Neal. Near Shannon limit performance of Low-Density Parity-Check codes. Electronics Letters, vol.32, No.18, Aug.,1996:1645～1646.
[5]S-Y Chung, G D. Forney, T. Richardson, and R. Urbanke. On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit. IEEE Commun. Letters, Feb.2001:58～60.
[6]J. Li, K. R. Narayanan, E. Kurtas, and C. N. Georghiades, "Product Accumulate Codes:A Class of Codes With Near-Capacity Performance and Low Decoding Complexity," IEEE Transaction On Information Theory, Vol.50, No.1, January 2004.
[7]R. M. Tanner. A recursive approach to low complexity codes. IEEE Trans. Inform. Theory, vol.27, Sept.1981:533～547.
[8]Frank R. Kschischang, Brendan J. Frey, and Hans-Andrea Loeliger. Factor graphs and the sum-product algorithm. IEEE Trans. Inform. Theory, vol.47, Feb.2001: 498-520.
[9]Elias P. Error-free coding. IEEE Transaction on Information Theory,1954,IT-4:29-37
[10]Pyndiah R, Glavieux, Picart A,et al. Near optimum decoding of product codes. IEEE GLOBECOM,1994,1:339-343
[11]Pyndiah R.Near optimum decoding of product codes:block turbo codes. IEEE Transaction on Communications,1998,46(8):1003-1010
[12]S. ten Brink. Convergence behavior of iteratively decoded parallel concatenated codes. IEEE Trans. Commun., Vol.49, Oct.2001:1727～1737.
[13]S. ten Brink. Convergence of iterative decoding. Electron. Lett.,1999,35, (lo), pp. 806-808
[14]L. Bahl, J. Cocke, F. Jelinek, and J. Raviv. Optimal decoding of linear codes for minimizing symbol error rate. IEEE Trans. Inform. Theory, Vol.20, Mar.1974: 284-287.
[15]N.Wiberg. Codes and decoding on general graphs. Ph.D. dissertation, Linkoping Univ., Sweden,1996.
[16]T. M. Cover and J. A. Thomas. Elements of Information Theory. New York:Wiley, 1991.
[17]R. W. Hamming. Coding and Information Theory. Englewood Cliffs, NJ: Prentice-Hall,1986.
[18]王琳,徐位凯.高效信道编译码技术.第一版,北京,人民邮电出版社,2007年4月.
[2]R. G Gallager. Low-density parity-check codes. IRE Trans. Inform. Theory, Jan. 1962:21-28.
[3]R. M. Tanner. A recursive approach to low complexity codes. IEEE Trans. Inform. Theory, vol. IT-27, Sept.1981:533～547.
[4]D.J.C.MacKay, R.M.Neal. Near Shannon limit performance of Low-Density Parity-Check codes. Electronics Letters, vol.32, No.18, Aug.,1996:1645～1646.
[5]S-Y Chung, G D. Forney, T. Richardson, and R. Urbanke. On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit. IEEE Commun. Letters, Feb.2001:58～60.
[6]J. Li, K. R. Narayanan, E. Kurtas, and C. N. Georghiades, "Product Accumulate Codes:A Class of Codes With Near-Capacity Performance and Low Decoding Complexity," IEEE Transaction On Information Theory, Vol.50, No.1, January 2004.
[7]R. M. Tanner. A recursive approach to low complexity codes. IEEE Trans. Inform. Theory, vol.27, Sept.1981:533～547.
[8]Frank R. Kschischang, Brendan J. Frey, and Hans-Andrea Loeliger. Factor graphs and the sum-product algorithm. IEEE Trans. Inform. Theory, vol.47, Feb.2001: 498-520.
[9]Elias P. Error-free coding. IEEE Transaction on Information Theory,1954,IT-4:29-37
[10]Pyndiah R, Glavieux, Picart A,et al. Near optimum decoding of product codes. IEEE GLOBECOM,1994,1:339-343
[11]Pyndiah R.Near optimum decoding of product codes:block turbo codes. IEEE Transaction on Communications,1998,46(8):1003-1010
[12]S. ten Brink. Convergence behavior of iteratively decoded parallel concatenated codes. IEEE Trans. Commun., Vol.49, Oct.2001:1727～1737.
[13]S. ten Brink. Convergence of iterative decoding. Electron. Lett.,1999,35, (lo), pp. 806-808
[14]L. Bahl, J. Cocke, F. Jelinek, and J. Raviv. Optimal decoding of linear codes for minimizing symbol error rate. IEEE Trans. Inform. Theory, Vol.20, Mar.1974: 284-287.
[15]N.Wiberg. Codes and decoding on general graphs. Ph.D. dissertation, Linkoping Univ., Sweden,1996.
[16]T. M. Cover and J. A. Thomas. Elements of Information Theory. New York:Wiley, 1991.
[17]R. W. Hamming. Coding and Information Theory. Englewood Cliffs, NJ: Prentice-Hall,1986.
[18]王琳,徐位凯.高效信道编译码技术.第一版,北京,人民邮电出版社,2007年4月.