Title :
Division-and-accumulation over GF(2m)
Author_Institution :
Dept. of Electr. & Comput. Eng., Waterloo Univ., Ont., Canada
fDate :
6/1/1997 12:00:00 AM
Abstract :
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(2m) 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
Keywords :
Galois fields; Reed-Solomon codes; digital arithmetic; encoding; Cauchy cells; Galois field division; Reed-Solomon codes; complex arithmetic operation; division-and-accumulation; hardware; high speed encoding; inversion; multiple stream DAA structure; multiplication; pipeline operations; sequential operation; throughput; time consuming; Arithmetic; Computational complexity; Concurrent computing; Encoding; Galois fields; Hardware; Pipelines; Reed-Solomon codes; Signal processing algorithms; Throughput;
Journal_Title :
Computers, IEEE Transactions on
