On Decoding Algebraic Codes Using Radical Locators
| Autor: | Chong-Dao Lee, Yan-Haw Chen, Yaotsu Chang, Tsung-Ching Lin, Trieu-Kien Truong |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Discrete mathematics
Polynomial Computer science Iterative method Diagonal 020206 networking & telecommunications 02 engineering and technology Library and Information Sciences Square matrix Computer Science Applications Matrix (mathematics) symbols.namesake Gaussian elimination 0202 electrical engineering electronic engineering information engineering symbols Coset Decoding methods Information Systems Sparse matrix |
| Zdroj: | IEEE Transactions on Information Theory. 66:6835-6854 |
| ISSN: | 1557-9654 0018-9448 |
| DOI: | 10.1109/tit.2020.2994905 |
| Popis: | It is well-known that the decoding of algebraic codes with error locators have been extensively conceived in the literature over a half century. The radical locator, which is an $\omega $ th root of error locator, has recently been discovered. This paper focuses on the two classes of radical locators. The first is complete radical locators , where all the locators are assigned to radical locators. The second is partial radical locators in that there are only a few locators being radical locators. In the former case based on complete radical locators, a new square matrix whose determinant is a univariate radical-locator polynomial is proposed. In particular, this matrix is modified to allow a large square matrix. It can be transformed by Gaussian elimination to the matrix in a row-echelon form in which zeros appearing in the diagonal entries of the current matrix are able to determine errors implicitly. Furthermore, this work further extends the previous results from the univariate case to multivariate cases. The matrix methods found herein enable one to decode a large class of cyclic codes efficiently. In the latter case, the cyclotomic cosets are a practical approach to select a small subset of positive integers. They are employed to develop partial radical locators. Finally, in contrast with the complete radical locators, the algebraic decoding methods make a natural use of partial radical locators more widely and flexibly to arbitrary cyclic codes. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|