Title :
Efficient bit-serial multiplication and the discrete-time Wiener-Hopf equation over finite fields
Author :
Morii, Masakatu ; Kasahara, Masao ; Whiting, Douglas L.
Author_Institution :
Dept. of Electron. & Inf. Sci., Kyoto Inst. of Technol., Japan
fDate :
11/1/1989 12:00:00 AM
Abstract :
Discrete-time Wiener-Hopf equations (DTWHEs) over finite fields are considered. It is shown that solving the DTWHE is equivalent to performing division over finite fields. The proof provides a new interpretation of the relationship between bit-serial multiplication and DTWHEs. The interpretation enables bit-serial multiplication over GF(2 m) to be understood more easily. As an example, bit-serial multiplication methods for multiplying any two elements that can be done without performing any transformation, or with only a simple transformation of the bases, are presented
Keywords :
digital arithmetic; discrete time systems; information theory; multiplying circuits; GF(2m); Reed-Solomon encoder; bit-serial multiplication; discrete-time Wiener-Hopf equation; finite fields; Arithmetic; Concatenated codes; Costs; Equations; Galois fields; Polynomials; Reed-Solomon codes; Throughput; Very large scale integration; Viterbi algorithm;
Journal_Title :
Information Theory, IEEE Transactions on
