CONSTRUCTION OF A DECODER FOR AN ALGEBRAIC GEOMETRY CODE

THE OBJECTIVE OF THIS PROJECT IS TO INITIATE THE DEVELOPMENT OF A NEW AND VERY POWERFUL FAMILY OF ERROR CORRECTING CODES (I.E., ALGEBRAIC GEOMETRY CODES FROM HERMITIAN CURVES), BY LAYING THE GROUNDWORK FOR THE IMPLEMENTATION OF ONE OF THE SHORTER CODES FROM THIS FAMILY. APPLICATIONS IN WHICH, FOR A VARIETY OF REASONS, SYMBOL SIZE IS CONSTRAINED TO FOUR BITS, ARE BEING ADDRESSED. ALGEBRAIC GEOMETRY CODES WITH THIS SYMBOL SIZE ARE SUPERIOR TO OTHER FOUR BIT CODES, YET THE DECODING PROCEDURE IS AMENABLE TO NEAR-TERM EXECUTION. DEVELOPMENT OF A NEAR-TERM PRODUCT FOR EARLY COMMERCIALIZATION BENEFITS THE LONGER TERM GOAL OF MORE BROADLY EXPLOITING THIS POWERFUL FAMILY OF CODES. THE RESEARCH IS BRINGING TOGETHER RECENT CONTRIBUTIONS FROM VARIOUS SOURCES TO DEFINE A DECODING ALGORITHM AND APPLY IT TO A SPECIFIC FOUR BIT CODE. THE DECODER STRUCTURE IS BEING DEFINED IN SUFFICIENT DETAIL TO ALLOW PRE-DESIGN OF THE DECODER HARDWARE. A COMPUTER SIMULATION OF THE DECODING ALGORITHM IS ALSO BEING DEVELOPED TO STUDY HERMITIAN CODE PERFORMANCE OVER A BROAD RANGE OF PARAMETER VALUES, ADDRESS TRADEOFF ISSUES, AND TO DEMONSTRATE THE PERFORMANCE OF THE CODE SELECTED FOR HARDWARE IMPLEMENTATION.