High-radix symbolic substitution and superposition techniques for optical matrix algebraic computations

Kai Hwang; Dhabaleswar Kumar Panda

doi:10.1117/12.59950

1 November 1992 High-radix symbolic substitution and superposition techniques for optical matrix algebraic computations

Kai Hwang, Dhabaleswar Kumar Panda

Author Affiliations +

Optical Engineering, Vol. 31, Issue 11, (November 1992). https://doi.org/10.1117/12.59950

Abstract

This paper presents a new 3-D digit-plane optical architecture for massively parallel matrix computations. This architecture decomposes matrix-structured data into digit planes using high-radix number representation and performs fast arithmetic on digit planes, exploiting spatial parallelism. While arithmetic operations are carried out using symbolic substitution, data manipulation operations (permutation, rotation, and translations) are carried out in parallel by a data manipulator using freespace optical interconnections. A new symbolic superposition technique is proposed to implement logical and set-theoretic operations on matrix-structured data in optics. The potential ofthis architecture is demonstrated to support structured matrix algebraic computation. We derive the complexity of symbolic substitution and symbolic superposition rules for radix-r arithmetic. The representational efficiency and the projected speed gain of high-radix arithmetic are compared against binary electronic matrix arithmetic.

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Kai Hwang and Dhabaleswar Kumar Panda "High-radix symbolic substitution and superposition techniques for optical matrix algebraic computations," Optical Engineering 31(11), (1 November 1992). https://doi.org/10.1117/12.59950

Published: 1 November 1992

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