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Partial Inverses mod $m(x)$ and Reverse Berlekamp?Massey Decoding.
- Source :
- IEEE Transactions on Information Theory; Dec2016, Vol. 62 Issue 12, p6737-6756, 20p
- Publication Year :
- 2016
-
Abstract
- This semi-tutorial paper introduces the partial-inverse problem for polynomials and develops its application to decoding Reed–Solomon codes and some related codes. The most natural algorithm to solve the partial-inverse problem is very similar to, but more general than, the Berlekamp–Massey algorithm. Two additional algorithms are obtained as easy variations of the basic algorithm: the first variation is entirely new, while the second variation may be viewed as a version of the Euclidean algorithm. Decoding Reed–Solomon codes (and some related codes) can be reduced to the partial-inverse problem, both via the standard key equation and, more naturally, via an alternative key equation with a new converse. Shortened and singly-extended Reed–Solomon codes are automatically included. Using the properties of the partial-inverse problem, two further key equations with attractive properties are obtained. The paper also points out a variety of options for interpolation. [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 62
- Issue :
- 12
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 119616346
- Full Text :
- https://doi.org/10.1109/TIT.2016.2613559