High accuracy optical processors: a new performance comparison

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

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.

Modified direct twos-complement parallel array multiplication algorithm for complex matrix operation

A direct twos-complement parallel array multiplication algorithm is introduced and modified for digital optical numerical computation. The modified version overcomes the problems encountered in the conventional optical twos-complement algorithm. In the array, all the summands are generated in parallel, and the relevant summands having the same weights are added simultaneously without carries, resulting in the product expressed in a mixed twos-complement system. In a two-stage array, complex multiplication is possible with using four real subarrays. Furthermore, with a three-stage array architecture, complex matrix operation is straightforwardly accomplished. In the experiment, parallel two-stage array complex multiplication with liquid-crystal panels is demonstrated.

Fiber-optic array algebraic processing architectures

A high-accuracy fiber-optic array processor (FOAP) based on the algorithm of digital multiplication by analog convolution is proposed. The FOAP architecture is a local regularly interconnected processor that utilizes an array of identical all-optical elemental-processing lattice units, namely, an optical splitter, an optical combiner, and a binary programmable fiber-optic transversal filter. Various FOAP matrix multipliers are proposed for nonnegative and twos-complement binary arithmetic matrix-vector, matrix-matrix, triple-matrix, and high-order matrix operations. The overall performances of the FOAP matrix multipliers are compared with the time-integrating and space-integrating architectures and with the digital multipliers. Extension of the digital-multiplication-by-analog-convolution algorithm is also considered.

Optical complex matrix-vector multiplication with negative binary inner products

Based on the mixed negative binary number system, we propose an inner-product algorithm for digital complex-valued matrix-vector multiplication. The features are no carries, no signs, no indications for decimal points, and simple preprocessing and postprocessing. Correspondingly, an optical architecture of incoherent optical correlation with spatial digital coding of data is suggested. Negative binary complex matrix-vector multiplication can be realized optically in parallel with a high accuracy. The experimental result is also given.

Negative binary arithmetic algorithms for digital parallel optical computation

Based on a negative binary number system, an algorithm with weighted-shifted addition, parallel-array multiplication, and a two-stage-array complex operation is proposed to carry out the multiplication of two complex numbers. The complex multiplication is performed without signs, carries, and recoding. The algorithm is suitable for optical implementation, and an optical parallel architecture is suggested. The experimental result is also given.

Error-correction coding for accuracy enhancement in optical matrix-vector multipliers

Error-correcting codes provide a technique for enhancing the accuracy of optical matrix-vector multipliers (OMVM's). The effects of signal-independent and signal-dependent noise on the performance of OMVM's that employ error-correcting codes are studied through the use of computer simulations. Noise present in the matrix results in random errors that can be corrected by these codes. Noise present in the vector results in nonrandom errors that are difficult to correct by using random error-correcting codes. The effect of code type is also investigated.

Smart Quasiserial post processor for optical systolic systems

A novel quasiserial post processor is proposed for improving the performance of optical systolic systems.

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.