Paper Info
Title
Inverse-free Berlekamp-Massey-Sakata Algorithm and Small Decoders for Algebraic-Geometric Codes
Abstract
This paper proposes a novel algorithm for finding error-locators of algebraic-geometric codes that can eliminate the division-calculations of finite fields from the Berlekam p- Massey-Sakata algorithm. This inverse-free algorithm provides full performance in correcting a certain class of errors, generic errors, which includes most errors, and can decode codes on alge- braic curves without the determination of unknown syndromes. Moreover, we propose three different kinds of architectures that our algorithm can be applied to, and we represent the control operation of shift-registers and switches at each clock- timing with numerical simulations. We estimate the performance in comparison of the total running time and the numbers of multipliers and shift-registers in three architectures wi th those of the conventional ones for codes on algebraic curves. Index Terms—codes on algebraic curves, syndrome decod- ing, Berlekamp-Massey-Sakata algorithm, Gr¨ obner basis, linear feedback shift-register.
Year
Venue
Keywords
2007
Clinical Orthopaedics and Related Research
information theory,finite field,numerical simulation,linear feedback shift register,indexing terms,generalization error,algebraic curve
Field
DocType
Volume
Algebraic geometric,Discrete mathematics,Inverse,Finite field,BCJR algorithm,Berlekamp–Welch algorithm,Algebraic curve,Block code,Algorithm,Berlekamp–Massey algorithm,Mathematics
Journal
abs/0705.0
Citations 
PageRank 
References 
0
0.34
13
Authors
2
Name
Order
Citations
PageRank
Hajime Matsui1188.14
Seiichi Mita231638.88