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Algebraic Decoding of Quasi-Reversible BCH Codes Using Band Matrices.
- Source :
-
IEEE Transactions on Communications . May2021, Vol. 69 Issue 5, p2800-2811. 12p. - Publication Year :
- 2021
-
Abstract
- A Bose-Chaudhuri-Hocquenghem (BCH) is called quasi-reversible if there are consecutive elements a1, . . . , a2 in the defining set, where a1 is a negative integer and a2 is a positive integer. A matrix in band form presented in this article involves the use of the Newton identities and symmetric polynomial identities. This matrix is the coefficient matrix of a linear system. The solution to such a linear system is the coefficients of an error-locator polynomial for quasi-reversible BCH codes. Its computational complexity is significantly lower than BCH decoding using the linear system with coefficient matrix in column echelon form. This article also proposes a new partial syndrome matrix with radical locators and a lot of zeros. Such a matrix is still in band form. The expansion of its matrix determinant is exactly a radical-locator polynomial. Compared to the former radical-locator polynomials in the literature, the newly discovered radical-locator polynomial not only requires less storage memory but also results in computational benefits. Surprisingly, the resulting polynomials are much sparser than those for the narrow-sense BCH codes. Finally, a complete algebraic decoding algorithm for quasi-reversible BCH codes is provided. The error-locator and radical-locator polynomials of degree less than or equal to 5 are listed. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00906778
- Volume :
- 69
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Communications
- Publication Type :
- Academic Journal
- Accession number :
- 150449007
- Full Text :
- https://doi.org/10.1109/TCOMM.2021.3059006