Algebraic Soft-Decision Decoding of Hermitian Codes

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 interpolati...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 56; no. 6; pp. 2587 - 2600
Main Authors: Lee, Kwankyu, O'Sullivan, Michael E.
Format: Journal Article
Language:English
Published: New York IEEE 01.06.2010
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algebra
Algebraic soft-decision decoding
Algorithm design and analysis
Algorithms
Codes
Computer simulation
Cryptography
Decoders
Decoding
Electronic circuits
Foundations
Geometry
Gröbner bases
Hermitian codes
Information analysis
Information theory
Interpolation
interpolation algorithm
Mathematics
Polynomials
Statistics
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Description
Summary: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.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2010.2046208