Advances in Applied Mathematics 31 420-432 2003年8月 [査読有り]
The combinatorics of reduced Gröbner bases of certain zero-dimensional ideals, which arise when Gröbner basis technique is applied to the soft-decision maximum likelihood decoding of binary linear block codes, will be studied.
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E86-A(3) 643-651 2003年3月 [査読有り]
New algorithms for the soft-derision and the hard-derision maximum likelihood decoding (MLD) for binary linear block codes are proposed. It has been widely known that both MLD can be regarded as an integer programming with binary arithmetic conditions. Recently, Conti and Traverso have proposed an efficient algorithm which uses Gröbner bases to solve integer programming with ordinary integer ar...
Proceedings of the 2002 IEEE International Symposium on Information Theory (IEEE ISIT2002) 316- 2002年2月 [査読有り]
The soft-decision maximum likelihood decoding belongs to integer programming with constraint linear equations to modular arithmetic. In this paper an algorithm to solve integer programming to modulus an arbitrary positive integer using Gröbner bases is proposed.
Proceedings of the 2002 IEEE International Symposium on Information Theory (IEEE ISIT2002) 144- 2002年2月 [査読有り]
A new algorithm for the soft-decision decoding of linear block codes is proposed. The algorithm uses the technique of the ordered-statistics decoding proposed by Fossorier and Lin (1995) to estimate a certain part of the transmitted code vector, while the remaining part is estimated by using the technique of the maximum-likelihood decoding.
Computer algebraic systems have a long history of being used for computation. One aspect of the systems which makes them powerful as a mathematical language is that it mixes efficient algorithms with computation. Other is graphical user interfaces, literally.
This talk is concerned another topics; dependability, usability concurrent and parallel computations for the computer algebra systems. To...
We are working with a company to research, design, develop and verify the network system. In the last year, we tried to prove security properties of the network system. In this year, we are trying to find bugs in the specifications of the system by a model-checking technique and to find bugs in the implementation of the system by testing. In this presentation, we report a case study of formal m...
It has been open problem whether the syndrome array for the key equation exists in the framework of Sudan's list decoding. If it does, the Berlekamp-Massey-Sakata(BMS) algorithm can be applied the decoding scheme. We solve this problem in the negative. Instead, we investigate an alternative approach to reduce the computational effort.
This paper introduces a procedure for decoding linear codes up to half the Feng-Rao bound which is defined by R.Pellikaan, G-L.Feng, K. K.Tzeng and T.R.N.Rao found the procedure, and they showed it was a generalization of the Berlekamp-Massey algorithm. We summarize this decoding methods from the view due to S.Miura's doctoral thesis.
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