HIGH-RADIX SYMBOLIC SUBSTITUTION AND SUPERPOSITION TECHNIQUES FOR OPTICAL MATRIX ALGEBRAIC COMPUTATIONS

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 free-space optical interconnections. A new symbolic superposition technique is proposed to implement logical and set-theoretic operations on matrix-structured data in optics. The potential of this 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.