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.我们分析和推广我们的原始推理算法，这已经提出，基于贝叶斯网络和图模型。然后，我们设计了一个新的算法来计算后验概率的概率模型，包括类的有效码。并从理论和仿真两个方面对算法进行了检验，取得了较好的效果.此外，我们还从微分几何、机器学习和统计学的角度检验了该算法的收敛性和准确性，并给出了理论上的理解。3.定义了广义后验概率分布，并给出了一个给定观测概率分布的不确定推理问题的数学表达式。事实证明，我们的推理方法的结果有很多的数学意义，这是非常重要的。通过减少算法的计算量和内存占用，并对算法进行了改进.我们ap ...更多信息 将该算法应用到扩展连接图上，提出了一种有效的并行置信传播算法。作为一个典型的应用，我们应用了我们的算法，这已经在2.，在LDPC码构造的扩展连接图上进行译码。我们从理论和实验两个方面研究了它的性质。我们将我们的扩展连接图用于卷积码和咬尾码，然后应用我们在2中提到的算法。用于解码两个代码。我们从数学和计算的角度来检验它的结果。我们应用我们的广义算法计算后验概率，这是已经提出的2001年，一个特殊的模型类，有收敛性的保证。整个过程既保证了数学意义，又保证了计算效率和内存占用.我们在2001年对解码算法进行了研究，并从理论和实验的角度进行了检验。少

项目成果

松嶋敏泰: "情報論的学習理論における数理モデル"人工知能学会誌. Vol.16,No.2. 252-255 (2001)

Toshiyasu Matsushima：“基于信息的学习理论中的数学模型”，人工智能学会杂志，第 16 卷，第 252-255 期（2001 年）。

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)。

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。

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。