The VLSI Implementation of a Reed—Solomon Encoder Using Berlekamp's Bit-Serial Multiplier Algorithm

Berlekamp has developed for the California Institute of Technology Jet Propulsion Laboratory (JPL) a bit-serial multiplication algorithm for the encoding of Reed-Solomon (RS) codes, using a dual basis over a Galois field. The conventional RS encoder for long codes often requires lookup tables to perform multiplication of two field elements. Berlekamp's algorithm requires only shifting and EXCLUSIVE OR operations. It is shown in this paper that the new dual-basis (255,223) RS encoder can be realized readily on a single VLSI chip with NMOS technology.