Title :
Efficient calculation of fixed polarity Reed-Muller expansions over GF(5) using extended dual polarity property
Author :
Falkowski, Bogdan J. ; Rahardja, Susanto ; Lozano, Cicilia C.
Author_Institution :
Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore, Singapore
Abstract :
The extended dual polarity property has been used to optimize Kronecker as well as quaternary fixed-polarity Reed-Muller (FPRM) expressions. In this paper, extension of this method to calculate FPRM polynomial expansions over GF(5) is presented. The new algorithm takes the truth vector of a 5-valued function as its input and proceeds to generate all of the function´s FPRM spectral coefficient vectors one by one in a certain sequence. The experimental results for this algorithm are compared with other methods and it was found that it is more efficient than other methods for some functions. The presented algorithm requires low memory storage.
Keywords :
Galois fields; Reed-Muller codes; computational complexity; digital arithmetic; multivalued logic; 5-valued function; FPRM polynomial expansions; FPRM spectral coefficient vectors; GF(5); Kronecker expressions; dual polarity property; fixed polarity Reed-Muller expansions; memory storage; quaternary FPRM expressions; truth vector; Block codes; Computational complexity; Error correction; Fault detection; Galois fields; Input variables; Optimization methods; Polynomials; Signal processing algorithms; Testing;
Conference_Titel :
Circuits and Systems, 2004. MWSCAS '04. The 2004 47th Midwest Symposium on
Print_ISBN :
0-7803-8346-X
DOI :
10.1109/MWSCAS.2004.1354132
