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.
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Performance Comparison for Case Studies of the Fiber-Optic Array-Processor Matrix–Vector Multiplier of Fig. 5 for 32-bit (m = 32) Multiplicationsa
Case
b
n
N
NADC
1/T (MHz)
MOPS
R1
Remarks
1
2
32
128
12
100
203.2
2.032
Constant clock rate 1/T, constant ADC bits NADC
2
4
16
28
12
100
90.3
0.903
3
8
11
7
12
100
33.3
0.333
4
2
32
128
12
100
203.2
2.032
Constant matrix dimension N
5
4
16
128
16
20
82.6
4.13
6
8
11
128
18
0.20
1.22
6.1
b is the base used, n is the digits of accuracy, N is the number of optical convolvers of Fig. 5, NADC is the ADC resolution bits, MOPS is mega operations per second, and R1 is the Psaltis–Athale ratio.
Table 2
Performance Comparison of Several Optical Matrix–Vector Multipliers
1-D SI, one-dimensional space integrating; 1-D TI, one-dimensional time integrating; FM, frequency multiplexed; 1-D OP, outer products with one-dimensional modulators; 2-D OP, outer products with two-dimensional modulators; FOAP, fiber-optic array processor of Fig. 5.
Parameters for the product of an M × N matrix and an N × 1 vector to n digits of accuracy.
Assuming a 100-MHz clock rate; MOPS, mega operations per second for (n = 32, M = N = 128).
Table 3
Performance Comparison of Several Optical Matrix–Matrix Multipliers
SI, space integrating; TI, time integrating; 1-D OP, outer products with one-dimensional modulators; 2-D OP, outer products with two-dimensional modulators; FOAP, fiber-optic array processor of Fig. 6.
Parameters for the product of an M × N matrix and an N × P vector to n digits of accuracy.
Assuming a 100-MHz clock rate; GOPS, giga operations per second for (n = 32, M = N = P = 128).
Tables (3)
Table 1
Performance Comparison for Case Studies of the Fiber-Optic Array-Processor Matrix–Vector Multiplier of Fig. 5 for 32-bit (m = 32) Multiplicationsa
Case
b
n
N
NADC
1/T (MHz)
MOPS
R1
Remarks
1
2
32
128
12
100
203.2
2.032
Constant clock rate 1/T, constant ADC bits NADC
2
4
16
28
12
100
90.3
0.903
3
8
11
7
12
100
33.3
0.333
4
2
32
128
12
100
203.2
2.032
Constant matrix dimension N
5
4
16
128
16
20
82.6
4.13
6
8
11
128
18
0.20
1.22
6.1
b is the base used, n is the digits of accuracy, N is the number of optical convolvers of Fig. 5, NADC is the ADC resolution bits, MOPS is mega operations per second, and R1 is the Psaltis–Athale ratio.
Table 2
Performance Comparison of Several Optical Matrix–Vector Multipliers
1-D SI, one-dimensional space integrating; 1-D TI, one-dimensional time integrating; FM, frequency multiplexed; 1-D OP, outer products with one-dimensional modulators; 2-D OP, outer products with two-dimensional modulators; FOAP, fiber-optic array processor of Fig. 5.
Parameters for the product of an M × N matrix and an N × 1 vector to n digits of accuracy.
Assuming a 100-MHz clock rate; MOPS, mega operations per second for (n = 32, M = N = 128).
Table 3
Performance Comparison of Several Optical Matrix–Matrix Multipliers
SI, space integrating; TI, time integrating; 1-D OP, outer products with one-dimensional modulators; 2-D OP, outer products with two-dimensional modulators; FOAP, fiber-optic array processor of Fig. 6.
Parameters for the product of an M × N matrix and an N × P vector to n digits of accuracy.
Assuming a 100-MHz clock rate; GOPS, giga operations per second for (n = 32, M = N = P = 128).