Systolic time-integrating acoustooptic binary processor

Carry-free vector-matrix multiplication on a dynamically reconfigurable optical platform

Applying the parallelism of optical computing, we present a novel method of vector-matrix multiplication (VMM) based on a new optical computing platform, the ternary optical computer, which can reconfigure any two-input trivalued logic optical processor at runtime, according to the decrease-radix design principle. In this work, we investigate a novel optical VMM (OVMM) using five logic operations with the modified signed-digit (MSD) number system. To simplify the computation process, we realize a carry-free optical addition in three steps, which is independent of the length of the operands. And a new implementation method is proposed that can be used to realize the MSD multiplication in parallel. Based on the generation of partial products in parallel and the binary-addition-tree algorithm, the multiplication can be implemented with the MSD addition. Our initial experiments have been performed to verify the proposed OVMM method. The results show that the proposed method of OVMM is feasible and correct.

Modified direct twos-complement parallel array multiplication algorithm for complex matrix operation

A direct twos-complement parallel array multiplication algorithm is introduced and modified for digital optical numerical computation. The modified version overcomes the problems encountered in the conventional optical twos-complement algorithm. In the array, all the summands are generated in parallel, and the relevant summands having the same weights are added simultaneously without carries, resulting in the product expressed in a mixed twos-complement system. In a two-stage array, complex multiplication is possible with using four real subarrays. Furthermore, with a three-stage array architecture, complex matrix operation is straightforwardly accomplished. In the experiment, parallel two-stage array complex multiplication with liquid-crystal panels is demonstrated.

Fiber-optic array algebraic processing architectures

A high-accuracy fiber-optic array processor (FOAP) based on the algorithm of digital multiplication by analog convolution is proposed. The FOAP architecture is a local regularly interconnected processor that utilizes an array of identical all-optical elemental-processing lattice units, namely, an optical splitter, an optical combiner, and a binary programmable fiber-optic transversal filter. Various FOAP matrix multipliers are proposed for nonnegative and twos-complement binary arithmetic matrix-vector, matrix-matrix, triple-matrix, and high-order matrix operations. The overall performances of the FOAP matrix multipliers are compared with the time-integrating and space-integrating architectures and with the digital multipliers. Extension of the digital-multiplication-by-analog-convolution algorithm is also considered.

Negative binary arithmetic algorithms for digital parallel optical computation

Based on a negative binary number system, an algorithm with weighted-shifted addition, parallel-array multiplication, and a two-stage-array complex operation is proposed to carry out the multiplication of two complex numbers. The complex multiplication is performed without signs, carries, and recoding. The algorithm is suitable for optical implementation, and an optical parallel architecture is suggested. The experimental result is also given.

Fast digital optical multiplication using an array of binary symmetric logic counters

Because of the lack of fast, accurate, and large dynamic range analog-to-digital converters (ADCs), optical implementation of the digital multiplication through analog convolution (DMAC) algorithm yields a slow digital multiplier. By replacing both the optical adder and ADC arrays by an optical combinatorial logic counter array, a new optical fast digital multiplication method is proposed. Compared to the existing optical DMAC scheme, the new method promises both higher processing speed and accuracy. A comparison of this and some of the other optical and electronic fast digital multiplication schemes is also presented.

Digital optical isochronous array processing

An optical isochronous array processing method is proposed. An optical isochronous array processor (OIAP) is a local regularly interconnected processing network that employs an array of identical optical processing elements. In an OIAP, incoming isochronous data are parallel processed in a fashion much like a propagating electromagnetic wavefront. For the various applications, the OIAP processing elements and their interconnections can be different. In this paper, various all-optical OIAP elements are considered. Applications ranging from optical binary number multiplication preprocessing to optical matrix algebra as well as to optical residue arithmetic are presented.