| Research Abstract |
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
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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
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