Designs of optoelectronic trinary signed-digit multiplication by use of joint spatial encodings and optical correlation

Trinary signed-digit (TSD) symbolic-substitution-based (SS-based) optical a dders, which were recently proposed, are used as the basic modules for desi gning highly parallel optical multiplications by use of cascaded optical co rrelators. The proposed multiplications perform carry-free generation of th e multiplication partial products of two words in constant time. Also, thre e different multiplication designs are presented, and new joint spatial enc odings for the TSD numbers are introduced. The proposed joint spatial encod ings allow one to reduce the SS computation rules involved in optical multi plication. In addition, the proposed joint spatial encodings increase the s pace-bandwidth product of the spatial light modulators of the optical syste m. This increase is achieved by reduction of the numbers of pixels in the j oint spatial encodings for the input TSD operands as well as reduction of t he number of pixels used in the proposed matched spatial filters for the op tical multipliers. (C) 1999 Optical Society of America.