DocumentCode :
50950
Title :
Linearized Polynomial Interpolation and Its Applications
Author :
Xie, Huan ; Lin, James ; Yan, Zhennan ; Suter, Bruce W.
Author_Institution :
Department of Electrical and Computer Engineering, Lehigh University, Bethlehem, PA, USA
Volume :
61
Issue :
1
fYear :
2013
fDate :
Jan.1, 2013
Firstpage :
206
Lastpage :
217
Abstract :
In this paper, we first propose an interpolation algorithm in a well ordered free module of a linearized polynomial ring, and then use this algorithm to decode several important families of codes, Gabidulin codes, Kötter and Kschischang (KK) codes and Mahdavifar and Vardy (MV) codes. Our decoding algorithm for Gabidulin codes is different from the polynomial reconstruction algorithm by Loidreau. When applied to decode KK codes, our interpolation algorithm is equivalent to the Sudan-style list-1 decoding algorithm proposed by Kötter and Kschischang for KK codes. The interpolation approach is also capable of solving the interpolation problem for the list decoding of MV codes proposed by Mahdavifar and Vardy, and has a lower complexity than Gaussian elimination. An interpolator for list decoding of MV codes has also been implemented in hardware and the synthesis results show that it leads to better throughput and efficiency than Gaussian elimination.
Keywords :
Complexity theory; Decoding; Error correction; Interpolation; Network coding; Polynomials; Vectors; Error control codes; interpolation; linearized polynomials; list decoding; module; network coding;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/TSP.2012.2222400
Filename :
6320677
Link To Document :
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