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The Partial-Inverse Approach to Linearized Polynomials and Gabidulin Codes With Applications to Network Coding
- Source :
- IEEE Transactions on Information Theory; 2023, Vol. 69 Issue: 6 p3759-3774, 16p
- Publication Year :
- 2023
-
Abstract
- This paper introduces the partial-inverse problem for linearized polynomials and develops its application to decoding Gabidulin codes and lifted Gabidulin codes in linear random network coding. The proposed approach is a natural generalization of its counterpart for ordinary polynomials, thus providing a unified perspective on Reed–Solomon codes for the Hamming metric and for the rank metric. The basic algorithm for solving the partial-inverse problem is a common parent algorithm of a Berlekamp–Massey algorithm, a Euclidean algorithm, and yet another algorithm, all of which are obtained as easy variations of the basic algorithm. Decoding Gabidulin codes can be reduced to the partial-inverse problem via a key equation with a new converse. This paper also develops new algorithms for interpolating crisscross erasures and for joint decoding of errors, erasures, and deviations in random network coding.
Details
- Language :
- English
- ISSN :
- 00189448 and 15579654
- Volume :
- 69
- Issue :
- 6
- Database :
- Supplemental Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Periodical
- Accession number :
- ejs63099458
- Full Text :
- https://doi.org/10.1109/TIT.2023.3236720