Rapid unbiased bipolar incoherent calculator cube

Abstract

Presented in this paper is one of several possible electrooptical engagement array architectures for performing matrix-matrix multiplication using incoherent light. Essential components of this new signal-processing device include two dynamic light valves operating in a reflection mode, a 2-D photodetector array, and a single polarizing beam splitter.

Modified engagement method for matrix operation

“…1 and 10-20. In this paper we use the engagement array as a PE array with local memory and a systolic array without local memory. We report that, based on two-dimensional ring interconnection topology, matrix-matrix multiplication can be efficiently performed with the engagement array, which involves fewer steps than those reported by Speiser and Whitehouse, 11 Bocker et al, 10 and Kung. 14 Figure 1 shows the Speiser-Whitehouse scheme for two 3 3 3 matrix-matrix multiplications.…”

“…2,8 Digital-encoding techniques, 4,5 which equivalently augment the processor size to increase accuracy, inflate the preprocessing and postprocessing costs 9 that are required to implement a matrix operation. However, the systolic and@or engagement array, which have been successfully implemented by VLSI technology, is worth studying, both from an optical view point 7,10 and an electronic view point. 1 Although the systolic and the engagement methods have been widely investigated, there are no formal and coherent definitions for the terms systolic array and engagement array.…”

“…1 Although the systolic and the engagement methods have been widely investigated, there are no formal and coherent definitions for the terms systolic array and engagement array. Speiser and Whitehouse, 11 Bocker et al, 10 and Whitehouse et al 12 coined the term engagement array to denote one specific type of matrix operation in which input matrices A, B enter an array in a specific engagement manner, and the processing elements 1PE's2 have local memory 1accumulation2, i.e., the calculated data 3c 1t2 5 c 1t212 1 ab4 are not moved to other cells. Fisher's definition of a systolic array requires that only boundary cells 13 can be input@output ports for the systems, i.e., the calculated data must be moved to the boundary cells.…”

“…Implementation of the PE can also be realized by other methods: an acousto-optic device, 7 the Bocker et al electro-optic implementation suggestion, 10 Yu's magneto-optic spatial light modulator, 23 analog processing elements, 2,8 binary-encoded algorithms, 4 or negative binary-encoded algorithms. 5 The local memory of the PE can be realized when ''the charges of the photodetector are accumulated'' as suggested by Bocker et al 10 The two-dimensional ring interconnections between PE's can be realized in optics in the following methods: the Wang et al one-dimensional ring interconnection topology 24 can be extended to the two-dimensional crossed-ring case.…”

“…5 The local memory of the PE can be realized when ''the charges of the photodetector are accumulated'' as suggested by Bocker et al 10 The two-dimensional ring interconnections between PE's can be realized in optics in the following methods: the Wang et al one-dimensional ring interconnection topology 24 can be extended to the two-dimensional crossed-ring case. Brenner and Lohmann 25 and Jahn and Dä schner 26 have suggested and demonstrated several implementation methods that incorporate optical ring interconnection networks, but they do not use the name ring; they refer to it as cyclic shifting.…”