Iterative Soft-Decision Decoding of Reed-Solomon Codes of Prime Lengths

A novel scheme is presented for encoding and decoding of Reed-Solomon codes of prime lengths. Encoding is performed on a collection of codewords which are mapped through Galois Fourier transform into a codeword in a low density parity-check code with a binary parity-check matrix for transmission. Using this matrix, a binary iterative soft-decision decoding algorithm is applied to jointly decode a collection of codewords in the Reed-Solomon code. By allowing information sharing among the received vectors corresponding to the code words in the collection, the proposed decoding scheme achieves superior performance over algorithms decoding individual Reed Solomon codewords including maximum likelihood decoding.