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BBC R&D White Paper WHP031

Reed-Solomon Error Correction
C.K.P. Clarke

Keywords
digital television, error-correcting codes, DVB-T, hardware implementation, Galois field arithmetic

Abstract
Reed-Solomon error correction has several applications in broadcasting, in particular forming part of the specification for the ETSI digital terrestrial television standard, known as DVB-T.

Hardware implementations of coders and decoders for Reed-Solomon error correction are complicated and require some knowledge of the theory of Galois fields on which they are based. This note describes the underlying mathematics and the algorithms used for coding and decoding, with particular emphasis on their realisation in logic circuits. Worked examples are provided to illustrate the processes involved.