Efficient Decoding of Hermitian Codes

Advisor: Prof. John Komo

By participating in this summer research project, the student will learn to analyze and develop tools to evaluate error control coded wireless communication system performance. Error control coding deals with the addition of redundant symbols to an existing data stream, in order to correct errors in the transmission of this data. The focus of this research will be on nonbinary block codes. Reed-Solomon codes are nonbinary block codes and have been used very successfully in wireless communication systems. Reed-Solomon codes (specifically extended Reed-Solomon codes) have the property that the block code length is equal to the symbol alphabet where each symbol may be considered as a group of bits. It is desirable to have a block length considerably longer than the symbol alphabet for increased error correcting performance. A class of codes that gives this desirable property of increased block length are the Hermitian codes whose block length is equal to the cube of r and alphabet size equal to the square of r. The application of Hermitian codes to wireless communication systems will be investigated.

Specifically, efficient decoding algorithms for hard decision decoding of Hermitian will be considered and the performance compared to Reed-Solomon codes of similar lengths. Significant improvement in error correcting performance is readily achievable with errors and erasures decoding of Reed-Solomon codes using side information. Errors and erasures decoding algorithms will be considered for Hermitian codes in this research and comparisons to Reed-Solomon error performance will be evaluated. This research will lead directly into graduate research since there is a need for efficient decoding algorithms using side information for Hermitian codes.