THE DESIGN OF REED-SOLOMON CODECS OVER THE DUAL BASIS

In this paper we consider the implementation of Reed-Solomon (RS) code cs. It is suggested that the most appropriate basis for RS codecs to o perate over is the dual basis. The bit-serial Berlekamp multiplier has long been known to be suitable for implementation in RS encoders, but here we also consider its use in RS decoders. The Berlekamp multiplie r was previously thought suitable only for use in constant multipliers because it operates over both the dual basis and the polynomial basis . However, work on establishing optimal dual bases to the polynomial b asis allows for the design of fast and hardware-efficient 2-variable i nput dual basis multipliers which can be utilized in RS decoders. Acco rdingly, we quantify the advantages of utilizing these dual basis mult ipliers throughout RS codecs. These multipliers have also been utilize d in the design of two codecs, a (15, 11) RS codec and a (31, 9) RS co dec.