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

Abstract

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.

A parallel optical implementation of arithmetic operations

“…Different technologies can be used to implement this switching behavior. Like some of the recent optical processors [36,37,39], the presented processor can use polarized light and liquid crystals for switching: both light sources can produce horizontally polarized light and the cells that block the light can change the polarization direction of light 90 degrees using liquid crystals. Then vertically polarized light can be ignored as blocked.…”

“…Diversity of supported operations: Almost all of the past optical processors implement a single arithmetic operations like addition [14,15,23,35,36,53,63], multiplication [70], or vector-matrix multiplication [29,38,39]. In this paper we implement different arithmetic operations, making it possible to perform various multi-step computational tasks.…”

“…In the last few years, there seems to be growing interest in parallel optical computing; researchers are trying to use optical devices, like liquid crystal, to implement parallel arithmetic operations like addition [35][36][37] and to improve the performance of optical vector-matrix multiplication [29,[38][39][40][41].…”

Design and implementation of the one-step MSD adder of optical computer

“…The standard MSD addition is realized with four transformations in three successive steps [16,17]. The truth table of these four transformations is shown in Table 1, where the T and T 0 transformation is used to obtain the carry bit of MSD addition, and the W and W 0 transformation is used to obtain the current bit of MSD addition.…”

Research and implementation of parallel artificial bee colony algorithm based on ternary optical computer

“…At present, TOC has a preliminary theoretical system and experimental platform [11][12][13][14][15][16]. Beginning with the idea of publishing TOC in 2003, after Decrease-Radix Design theory [17], TOC encoder and decoder [18], FFT algorithm implementation and DFT algorithm implementation [19,20], performance analysis of a TOC [21], improved symbol number (MSD) adder [22][23][24][25][26], the implementation of reconfigurable ternary optical processor [27,28] and vector matrix multiplication [29,30], cellular automata [31] and other TOC-based applications, the current TOC has the conditions to implement parallel ABC algorithm.…”