Iterative Soft Input Soft Output Decoding of Reed-Solomon Codes by Adapting the Parity Check Matrix

An iterative soft input soft output (SISO) decoding algorithm for Reed-Solomon (RS) codes using their binary image representations is presented. The novelty of the iterative algorithm is in reducing a submatrix corresponding to the less reliable bits in the binary parity check matrix of the RS code to a sparse nature before each decoding iteration. The proposed algorithm can geometrically be interpreted as a gradient descent with the adaptive potential function. This adaptive procedure is crucial to the convergence behavior of the gradient descent algorithm and therefore greatly improves the decoding performance. Simulation results show that the proposed decoding algorithm and its variations provide significant gain over hard decision decoding (HDD) and compares favorably with other popular soft decision decoding methods both in terms of error performance and complexity.