Effects of error sources on the parallelism of an optical matrix-vector processor.

The error sources in a high accuracy optical matrix-vector processor are analyzed by numerical simulation in terms of their effects on the parallelism and speed of the processor. These effects are detailed for radices -2, -4 and -8. Radix -4 is shown to provide maximum parallel processing capabilities under the effects of the system's error sources. Processing speed is shown to be a function of matrix partitioning and the number of parallel processing channels. Consequently, radix -4 operation provides a higher processing speed than radix -2 and -8 for most matrix-vector multiplications when error source effects are considered.

Optical systems for digit-serial computation.

Optical systems and algorithms are presented for implementing digit-serial (or on-line) computations. These systems achieve high accuracy without the need for A-Ds and incorporate parallelism and carry-free addition to achieve high processing speed. On-line arithmetic allows parallel calculations to be performed by concurrent execution of operations. (Consecutive operations can start before all digits of the previous operations are available.) The algorithms are problem- and step-invariant and inherently allow variable precision as we show. To achieve parallelism, we introduce the modified signed-digit number representation into these algorithms and architectures. This results in new arithmetic rules (new addition rules, a different number of bits needed, a different number of cycles required) from those in conventional digital digit-serial systems. We include sufficient detail (not readily available elsewhere) needed for the design of the units we include. New architectures using optical bistable devices and optical interconnects are described that can implement digit-serial addition, subtraction, multiplication, and division algorithms in this new approach.