| Co-Investigator(Kenkyū-buntansha) |
KURIHARA Masazumi The University of Electro-Communications, Faculty of Electro-Communications, Research Assistant, 電気通信学部, 助手 (90242346)
FUJISAWA Masaya The Tokyo University of Science, Faculty of Engineering, Research Assistant, 第二工学部, 助手 (10345431)
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| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2005: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2004: ¥1,900,000 (Direct Cost: ¥1,900,000)
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| Research Abstract |
The objective of this research is to develop efficient algorithms for decoding not only algebraic geometric (AG) codes but also generalized algebraic geometric (GAG) codes and furthermore aim at systematizing past and new research results of fast decoding methods for those codes so that these decoding methods can be used practically in digital communication systems in the highly information-technological world in near future.
As outcomes of our researches, we have clarified several relations among fast decoding methods of those codes. In particular, we have shown that the parallel Berlekamp-Massey (BM) algorithm and Euclidean algorithm for decoding are identical, and that the multiple-sequence BM algorithm can be replaced by a succession of single-sequence BM algorithm. Furthermore, we have shown that the Welch-Belekamp algorithim can be realized as a vectorial version of BM algorithm. We presented these results in the 2004 International Symposium on Information Theory and Applications (ISITA-2004), in Parma, Italy, October 10-13, 2004, in the IEEE 2005 International Symposium on Information Theory, in Adelaide, Australia, September 4-9, 2005, and in the 2006 International Symposium on Information Theory and Applications (ISITA-2006), in Seoul, Korea, October 29-November 1, 2006, respectively. Related to the research, we published a textbook on Coding Theory entitled Introduction to Error-Correcting Codes which is a Japanese translation of A Course in Error-Correcting Codes by J.Justesen, and T.Hoeholdt published by European Mathematical Society, in 2004, as well as a paper entitled "Systolic array architecture implementing Berlekamp-Massey-Sakata algorithm for decoding codes on a class of algebraic curves" in IEEE Transactions on Information Theory, in 2005. In 2006, we had several tutorial lectures to give a grand survey of past and new results of our researches on fast decoding of AG codes.
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