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

1.对已提出的基于贝叶斯网络和图模型的推理算法进行了分析和推广。然后，我们设计了一种新的算法来计算包含有效码类的概率模型的后验概率。并从理论和仿真两个方面对该算法进行了检验，取得了较好的效果。从微分几何、机器学习和统计学的角度对算法的收敛和精度进行了检验，并给出了理论上的理解。定义了广义后验概率分布，给出了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具有许多非常重要的数学意义。对算法进行了改进，减少了计算量和内存占用，并对算法进行了程序瘫痪。WE AP…然后将该算法应用于扩展的联结图上，提出了一种高效的并行信任传播算法。作为一个典型的应用，我们将文[2]中提到的算法应用于LDPC码构造的扩展结图的译码。我们从理论和实验两个方面考察了它的性质。我们对卷积码和咬尾码都使用了我们的扩展连接图，然后我们应用2.中提到的算法对这两种码进行了译码。我们从数学和计算两个角度对其结果进行了检验。我们将我们于2001年提出的计算后验概率的推广算法应用于一类具有收敛保证的特殊模型类。整个过程既保证了数学意义，又保证了高效的计算和内存占用。我们于2001年提出了译码算法的研究成果，并从理论和实验的角度进行了检验。较少

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