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European Conference on Optical Communication

Multidimensionally-Encoded High-Precision Optical Multiplier for Matrix Multiplication

Pierre Nay, Xiansong Meng, Mingyang Gao, Kwangwoong Kim, Po Dong, Hao Hu, Deming Kong

Published Sep 28, 2025• 0 citations
Publisher

Abstract

We propose and demonstrate a proof-of-concept optical multiplier for matrix multiplication using multidimensional encoding to increase the numerical precision. We achieve error-free performance for 8-bit image processing, and a low error rate of$8.76 \times 10^{-5}$for 8-bit random number multiplication.

DOI
10.1109/ecoc66593.2025.11263052

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We propose and demonstrate a proof-of-concept optical multiplier for matrix multiplication using multidimensional encoding to increase the numerical precision. We achieve error-free performance for 8-bit image processing, and a low error rate of8.76×10−58.76 \times 10^{-5}8.76×10−5for 8-bit random number multiplication.
Optical algebraic processors can perform complex calculations in parallel and at high speeds. However, they commonly suffer from a low analog accuracy which hinders their widespread application. Error detection and correction codes provide one technique for improving the accuracy of optical algebraic processors. The use of these codes would allow some of the errors that may occur during a computation to be detected and possibly corrected. This paper describes the results of various computer simulations of optical matrix-vector multipliers employing error-correction codes. It discusses the application of convolutional codes to optical matrix-vector multipliers along with several block codes. Both binary and nonbinary codes are considered. The results indicate that a significant improvement in performance can be obtained when compared with processors not employing error-correction codes. Also, the type of noise, whether signal-independent or signal-dependent noise, has a significant effect on the performance of a matrix-vector multiplier employing an error code. The encoding and decoding operations required for the error codes can be performed optically.
Optical algebraic processors can perform complex calculations in parallel and at high speeds. However, they commonly suffer from a low analog accuracy which hinders their widespread application. Error detection and correction codes provide one technique for improving the accuracy of optical algebraic processors. The use of these codes would allow some of the errors that may occur during a computation to be detected and possibly corrected. This paper describes the results of various computer simulations of optical matrix-vector multipliers employing error-correction codes. It discusses the application of convolutional codes to optical matrix-vector multipliers along with several block codes. Both binary and nonbinary codes are not employing error-correction codes. Also, the type of noise, whether signal-independent or signal-dependent, has a significant effect on the performance of a matrix-vector multiplier employing an error code. The encoding and decoding operations required for the error codes can be performed optically.
Abstract An RSFQ flexible-precision multiplier is proposed. The circuit can perform multiplication with specified bit-width within a predefined bit range. The calculation bit-width can be changed in every operation. When the bit-width of a calculation decreases, the latency in cycles is reduced. The proposed circuit calculates the multiplication result with bit-level processing to save the circuit area. The circuit carries out multiplication by counting pulses on a signal line. An RSFQ flexible-precision matrix multiplication circuit based on the proposed multiplier is also proposed. Its internal multipliers share many component circuits and it is implemented in a compact area.
Optical matrix-vector multipliers are known to suffer from low computational accuracy which is the major drawback preventing them from becoming a practical force in real world applications. Error-correction coding is one technique proposed to overcome this problem of low level accuracy. In this thesis, the effects of the application of multiple error-correction codes to optical matrix-vector multipliers are studied. For this purpose, many different cases were simulated on a computer. Noting that an optical matrix-vector multiplier performs the product y = Ax, basically four cases were considered; signal independent and signal dependent noise in the matrix A, and signal independent and signal dependent noise in the vector x. Two different error-correcting codes were simulated; one being a binary, multiple error-correcting BCH code and other being a non-binary, multiple error-correcting Reed-Solomon code, which is basically an extension of the binary BCH code. The advantages and disadvantages of switching from binary BCH codes to non-binary Reed-Solomon codes were investigated. Based on the results obtained from the simulations, the conditions under which the use of error-correction coding is feasible in optical matrix-vector multipliers are discussed.