Iterative Decoding of Reed-Solomon Codes based on Non-binary Matrices

A novel iterative approach for soft-decision decoding of Reed-Solomon codes is presented that employs symbol-level belief propagation on an alternative parity-check matrix representation of the code. Construction of a suitable matrix is discussed from the viewpoint of iterative decoding, and certain conditions are derived on existence of structures detrimental for decoding. Simulation results demonstrate that the novel scheme performs substantially better than hard-decision decoding, especially with high rate codes, while being of much lower complexity than existing soft-decision decoding methods. Proposed method is also well-suited for efficient hardware implementations.