有限平面LDPC码的停止集

夏树涛; 胡懋智

doi:10.3724/SP.J.1146.2005.01328

有限平面LDPC码的停止集

doi: 10.3724/SP.J.1146.2005.01328

基金项目:

国家自然科学基金(60402031)和国家重点基础研究发展计划973 (2003CB314805)资助课题

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出版历程
- 收稿日期: 2005-10-24
- 修回日期: 2006-04-19
- 刊出日期: 2007-06-19

On the Stopping Sets of Finite Plane LDPC Codes

摘要

摘要: 有限平面LDPC码是一类重要的有结构的LDPC码，在利用和积算法(SPA)等迭代译码方法进行译码时表现出卓越的纠错性能。众所周知，次优的迭代译码不是最大似然译码，因而如何对迭代译码的性能进行理论分析一直是LDPC码的核心问题之一。近几年来，Tanner图上的停止集(stopping set)和停止距离(stopping distance)由于其在迭代译码性能分析中的重要作用而引起人们的重视。该文通过分析有限平面LDPC码的停止集和停止距离，从理论上证明了有限平面LDPC码的最小停止集一定是最小重量码字的支撑，从而对有限平面LDPC码在迭代译码下的良好性能给出了理论解释。
- 低密度校验(LDPC)码;有限几何;迭代译码;停止集;停止距离
Abstract: Finite plane LDPC codes are important structured LDPC codes, which have excellent performance under iterative decoding algorithm. It is a key problem that to evaluate the performance of LDPC codes under iterative decoding. Recently, the stopping sets and stopping distance of Tanner graph are of interests in performance evaluation. In this paper, the smallest sets of finite plane LDPC codes are studied. It shows that for finite plane LDPC codes, a smallest stopping set is the support of a codeword. These results give positive consequences for the good performance of finite plane LDPC codes under iterative decoding.

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Kschischang F R, Frey B J, and Loeliger H A. Factor graphs and the sum-product algorithm[J].IEEE Trans. on Inform. Theory.2001, 47(2):498-519[2]Kou Y, Lin S, and Fossorier M P C. Low-density parity-check codes based on finite geometries: a rediscovery and new results[J].IEEE Trans. on Inform. Theory.2001, 47(7):2711-2736[3]Tang H, Xu J, Lin S, and Abdel-Ghaffar K A S. Codes on finite geometries[J].IEEE Trans. on Inform. Theory.2005, 51(2):572-569[4]Lin S and Costello DJ. Error Control Coding: Fudamentals and Applications, 2nd Ed, Upper Saddle River, NJ: Prentice-Hall, 2004, Chap. 8: 273-282.[5]Di C, Proietti D, Telatar I E, Richardson T J, and Urbanke R L. Finite-length analysis of low-density parity-check codes on the binary erasure channel[J].IEEE Trans. on Inform. Theory.2002, 48(6):1570-1579[6]Kashyap N and Vardy A. Stopping sets in codes from designs. in Proc. IEEE Int. Sym. Inform. Theory, Yokohama, Japan, Jul. 2003: 122.[7]Schwartz M and Vardy A. On the stopping distance and the stopping redundancy of codes[J].IEEE Trans. on Inform. Theory.2006, 52(3):922-932[8]Koetter R and Vontobel PO. Graph covers and iterative decoding of finite-length codes. In Proc. 3rd Int. Symp. Turbo Codes and Related Topics, Brest, France, Sept. 2003: 75-82.[9]Feldman J, Wainwright M J, and Karger D R. Using linear programming to decode binary linear codes[J].IEEE Trans. on Inform. Theory.2005, 51(3):954-972[10]Chaichanavong P and Siegel PH. Relaxation bounds on the minimum pseudo-weight of linear codes. In Proc. IEEE Int. Symp. Inform. Theory, Sept. Adelaide, Australia 2005: 805-809.[11]Vontobel P O and Koetter R. Lower bounds on the minimum pseudo-weight of linear codes. In Proc. IEEE Int. Symp. Inform. Theory, Chicago, U.S.A., 2004: 70.[12]Vontobel P O, Smarandache R, and Kiyavash N, et al.. On the minimal pseudo-codewords of codes from finite geometries. In Proc. IEEE Int. Symp. Inform. Theory, Adelaide, Australia, Sept. 2005: 980-984.

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