| 引用本文: | 许拔,何英亮,周昌术,等.BSC信道下线性分组码的差错概率下界分析.[J].国防科技大学学报,2011,33(3):115-120.[点击复制] |
| XU Ba,He Yingliang,ZHOU Changshu,et al.Analysis of Lower Bound for the Error Probability of Linear Block Codes over the BSC Channel[J].Journal of National University of Defense Technology,2011,33(3):115-120[点击复制] |
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| BSC信道下线性分组码的差错概率下界分析 |
| 许拔1,2, 何英亮3, 周昌术4, 张尔扬1 |
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(1.国防科技大学 电子科学与工程学院， 湖南 长沙 410073;2.总参第六十三研究所，江苏 南京 210007;3.国防科技大学 计算机学院，湖南 长沙410073;4.湖南省军区预备役师通信科，湖南 长沙 410016)
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| 摘要: |
| 针对BSC信道，提出了一种线性分组码的最大似然译码差错概率下界的计算方法。根据最大似然译码算法原理，首先将译码差错概率转化为差错事件的联合概率， 基于改进的Dawson-Sankoff界的优化准则，推导出BSC信道下线性分组码差错冗余事件的判决准则，最后得到差错概率下界的计算表达式。该下界只依赖于码字的Hamming重量分布与信道的交叉概率。针对不同的LDPC码的仿真结果表明：较之常见的下界和sphere packing bound，本算法得到的下界性能更好、计算复杂度 更低。 |
| 关键词: LDPC 最大似然译码 Hamming重量分布函数 优化准则 |
| DOI： |
| 投稿日期：2010-09-18 |
| 基金项目: |
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| Analysis of Lower Bound for the Error Probability of Linear Block Codes over the BSC Channel |
| XU Ba1,2, He Yingliang3, ZHOU Changshu4, ZHANG Eryang1 |
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(1.College of Electronic Science and Engineering, National Univ. of Defense Technology，Changsha 410073, China;2.The 63rd Research Institute of PLA General Staff Headquarter, Nanjing 210007, China;3.Colleges of Computer, National Univ. of Defense Technology, Changsha 410073, China;4.The Communication Section of Reserve Division, Hunan Military Region, Changsha 410016, China)
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| Abstract: |
| A lower bound on the error rate of linear binary block codes (under maximum likelihood decoding) over BSC channels is proposed. According to the principle of the maximum likelihood (ML) decoding algorithm, the decoding error probability is firstly converted into the joint probability of the error events, and the judge rule of the redundant error events is deduced based on the optimization rule of the improved Dawson-Sankoff bound. Moreover, the calculation expression about lower bound of the error probability solely depends on the Hamming weight enumerator function of the code and the crossover probability of the channel. The simulation results applying to various LDPC codes show that the new lower bound outperforms those generic lower bounds and the sphere packing bound. Its computational complexity is also lower. |
| Keywords: low density parity check codes maximum likelihood decoding hamming weight enumerator function optimization rule |
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