Fast decoding methods of algebraic geometry codes and generalized algebraic geometry codes

代数几何代码和广义代数几何代码的快速解码方法

基本信息

批准号：
16560323
负责人：
SAKATA Shojiro
金额：
$ 2.24万
依托单位：
The University of Electro-Communications
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2006
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16560323/
关键词：
information and communication engineering algebra algebraic geometry code fast decoding method BMS algorithm generalized algebraic geometry code list decoding error-correcting code 補間多項式と因数分解 Berlekamp-Masseyアルゴリズム複数配列に対するBMアルゴリズム

项目摘要

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.

这项研究的目的是开发有效的算法，不仅解码代数几何（AG）代码，还可以开发广义的代数几何（GAG）代码，并进一步旨在系统化过去和新的研究结果，以使这些代码的快速解码方法能够实现这些解码方法的快速解码方法，以使我们在数字上进行了近距离的技术，即在我们的数字沟通中逐渐逐渐涉及，从而实现了无效的信息。已经阐明了这些代码的快速解码方法之间的几个关系。特别是，我们已经表明，用于解码的平行Berlekamp-Massey（BM）算法和欧几里得算法是相同的，并且可以通过一系列单个单序BM算法来代替多序列BM算法。此外，我们已经证明了Welch-Belekamp算法可以实现为BM算法的矢量版本。 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,分别是2006年。 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代数曲线”在2005年的IEEE信息理论交易中。2006年，我们进行了几次教程讲座，以对我们的过去和快速解码AG代码的研究的过去和新结果进行大量调查。