A Versatile Time-Domain Reed-Solomon Decoder

A versatile Reed-Solomon (RS) decoder structure is developed based on the time-domain decoding algorithm (transform decoding without transforms). In this paper, the algorithm is restructured and a method is given to decode any RS code generated by any generator polynomial. The main advantage of the introduced decoder structure is the versatility. By versatile decoder we mean a decoder that can be programmed to decode any Reed-Solomon code defined in Galois field 2'" with a fixed symbol size m. This decoder can correct both errors and erasures for any RS code including shortened and singly extended codes. It is shown that the introduced versatile decoder has a very simple structure and can be used to design high-speed singlechip VLSI decoders. As an illustrative example, a Gate-Array-Based programmable RS decoder is implemented on a single chip. This decoder chip can decode any RS code defined in GF (2') with any code word length and any number of information symbols. The decoder chip is fabricated using low power, 1.5 1, 2-layer metal, HCMOS technol-