Algebraic Soft-Decision Decoding of Hermitian Codes
Kwankyu Lee, Michael E. O'Sullivan
TL;DR
This paper introduces an algebraic soft-decision decoding method for Hermitian codes, adapting existing frameworks from Reed-Solomon codes, and demonstrates its effectiveness through simulations.
Contribution
It extends Koetter and Vardy's soft-decision decoding framework to Hermitian codes with a new algebraic foundation and interpolation algorithm.
Findings
Favorable performance of Hermitian codes over Reed-Solomon codes in simulations
Development of an algebraic foundation for soft-decision decoding of Hermitian codes
Introduction of an interpolation algorithm for the Q-polynomial
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-Solomon codes, to Hermitian codes. First we provide an algebraic foundation for soft-decision decoding. Then we present an interpolation algorithm finding 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-Solomon codes, favorable to the former.
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Taxonomy
TopicsCoding theory and cryptography · Error Correcting Code Techniques · Cryptographic Implementations and Security