The Analysis and Design of the Reliable Iterative Decoding Algorithm based on Uncertain Reasoning

基于不确定推理的可靠迭代译码算法分析与设计

• 批准号: 12650400
• 负责人: MATSUSHIMA Toshiyasu
• 金额: $ 2.24万
• 依托单位: Waseda University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12650400/
• 关键词: Uncertain Reasoning; Decoding Algorithm; Bayesian Network; Graphical Model; Probability Model; Posterior Probability Calculation; 複合アルゴリズム

1. We analyzed and generalized our original reasoning algorithm, which is already proposed, based on both Bayesian Network and Graphical Model. Then, we designed a new algorithm for calculating posterior probability on probability models including classes of efficient codes. We also inspected the algorithm in terms of both theoretical and simulating points and then got good results.2. Moreover, we inspected both convergence and accuracy of the algorithm in terms of the differential geometry, machine learning and statistics and then we gave theoretical understandings onto it.3. We defined the generalized posterior probability distribution and made mathematical expression of a problem of the uncertain reasoning given the observed probability distribution. It turned out that the result of our reasoning method has a lot of mathematical meanings that is very important. We improved our algorithm by reducing both the calculation and memory occupation, and by paralyzing its procedures.4. We ap … More plied our algorithm on the Extended Junction Graph, which is also our generalized original graph, then proposed the efficient parallel belief propagation algorithm. As a typical application, we applied our algorithm, which is already mentioned in 2., for decoding on Extended Junction Graph constructed by LDPC codes. We examined its natures in terms of both theoretical and experimental aspects.5. We used our Extended Junction Graph for both convolution codes and tail biting codes, then we applied our algorithm mentioned in 2. for decoding both codes. We examined its results from the both mathematical and computational points of view.6. We applied our generalized algorithm for calculating posterior probability, which is already proposed year 2001, to a special model class that has guarantee of convergence. The whole procedure guarantees mathematical meanings as well as both efficient calculation and memory occupation.7. We developed out results in year 2001 on decoding algorithm, then inspected from point of theoretical and experimental view. Less

1。我们根据贝叶斯网络和图形模型分析并概括了已经提出的原始推理算法。然后，我们设计了一种新算法，用于计算包括有效代码类别的概率模型的后验概率。我们还根据理论和模拟点检查了算法，然后获得了良好的结果。2。此外，我们根据差异几何形状，机器学习和统计数据检查了算法的收敛性和准确性，然后我们对其进行了理论理解。3。我们定义了普遍的后验概率分布，并在观察到的概率分布的情况下使不确定推理问题的数学表达。事实证明，我们推理方法的结果具有很多非常重要的数学含义。我们通过减少计算和记忆的发生以及瘫痪其程序来改善算法。4。我们…在扩展的连接图上更加将我们的算法（也是我们的广义原始图）上提出，然后提出了有效的平行信念传播算法。作为典型应用程序，我们应用了我们的算法，该算法已在2中提到。我们从理论和实验方面都检查了其本性。5。我们将扩展的连接图用于卷积代码和尾部咬合代码，然后我们应用了2中提到的算法。解码这两个代码。我们从数学和计算的观点检查了它的结果6。我们将广义算法应用于计算后验概率（2001年已经提出的），以保证收敛的特殊模型类。整个过程保证了数学含义以及有效的计算和记忆职业。7。我们在2001年开发了关于解码算法的结果，然后从理论和实验观点进行了检查。较少的

项目成果

Yoshifumi Ukita, Toshiyasu Matsushima, and Shigeichi Hirasawa: "On Learning Boolean Function using Fourier Transformation"Technical Report of The Institute of Electronics, Information and Communication Engineers. (COMP2000-56). 49-55 (2000)

Yoshifumi Ukita、Toshiyasu Matsushima 和平泽茂一：“On Learning Boolean Function using Fourier Transformation”电子信息通信工程师学会的技术报告。

Masaki Kiahara, Ryo Nomura and Toshiyasu Matsushima: "On the Application of Bayesian Method of Noise Reduction using Wavelet Packets"Technical Report of The Institute of Electronics, Information and Communication Engineers. (DSP2000-134). 9-16 (2000)

Masaki Kiahara、Ryo Nomura 和 Toshiyasu Matsushima：《论使用小波包的贝叶斯降噪方法的应用》电子信息通信工程师学会的技术报告。

野村亮: "メモリ量を低減した近似ベイズ符号化アルゴリズム"電子情報通信学会論文誌A. Vol.85-A, No.5. 46-59 (2003)

Ryo Nomura：“减少内存量的近似贝叶斯编码算法”IEICE Transactions A. Vol.85-A，No.5 (2003)。

野村亮: "メモリ量を低減した近似ベイズ符号化アルゴリズム"電子情報通信学会論文誌A. Vol.J85-A, No.5. 46-59 (2003)

Ryo Nomura：“减少内存量的近似贝叶斯编码算法”IEICE Transactions A. Vol.J85-A，No.5 (2003)。

Takahiro Yoshida, Toshiyasu Matsushima, and Shigeichi Hirasawa: "A Formulation of Distributed Corporative Problem based on Multi-terminal Systems"TECHNICAL REPORT OF IEICE. Vol 101, No 177, IT2001-17. 37-42 (2001)

Takahiro Yoshida、Toshiyasu Matsushima 和 Shigeichi Hirasawa：“基于多终端系统的分布式合作问题的表述”IEICE 技术报告。