Title :
Algebraic Soft-Decision Decoding of Hermitian Codes
Author :
Lee, Kwankyu ; O´Sullivan, Michael E.
Author_Institution :
Dept. of Math., Chosun Univ., Gwangju, South Korea
fDate :
6/1/2010 12:00:00 AM
Abstract :
An algebraic soft-decision decoder for Hermitian codes is presented. We apply Koetter and Vardy´s soft-decision decoding framework, now well established for Reed-Solmon codes, to Hermitian codes. First we provide an algebraic foundation for soft-decision decoding. Then we present an interpolation algorithm to find the Q-polynomial that plays a key role in the decoding. With some simulation results, we compare performances of the algebraic soft-decision decoders for Hermitian codes and Reed-Solmon codes, favorable to the former.
Keywords :
Hermitian matrices; algebraic codes; decoding; interpolation; polynomials; Hermitian code; Koetter-Vardy soft-decision decoding; Q-polynomial; algebraic soft-decision decoding; interpolation algorithm; Algebra; Algorithm design and analysis; Codes; Decoding; Electronic circuits; Geometry; Information analysis; Interpolation; Mathematics; Statistics; Algebraic soft-decision decoding; Gröbner bases; Hermitian codes; interpolation algorithm;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2010.2046208
