Division-and-accumulation over GF(2/sup m/)

The Galois field division is a complex arithmetic operation. The corresponding division-and-accumulation (DAA) is not only complex but also a time consuming operation. In this article, the DAA over GF(2/sup m/) is considered, and a simple scheme for its sequential operation is presented. A multiple stream DAA structure is developed which supports pipeline operations and yields an increased throughput with only a modest increase in the hardware. As an application, the use of the sequential DAA algorithm is shown for the high speed encoding of Reed-Solomon codes.