This Article 
 Bibliographic References 
 Add to: 
The Design of an Optoelectronic Arithmetic Processor Based on Permutation Networks
February 1997 (vol. 46 no. 2)
pp. 142-153

Abstract—This paper introduces a new concept by which it is possible to design and implement arithmetic processors using permutation networks. To demonstrate this concept, several optoelectronic arithmetic units combining optical directional coupler switches and cyclic permutation networks are designed. The designs show that addition, subtraction, and multiplication can all be performed in O(log n) time in residue code domain and using O(n2) directional coupler switches and gates, where n = log M, and M is the integer range of interest. These arithmetic units also have the capability of concurrent error detection and fault-tolerance, and they can be used to construct constant time inner product processors.

[1] A.F. Benner et al., "Digital Optical Counter Using Directional Coupler Switches," Applied Optics, vol. 30, no. 29, pp. 4,179-4,189, Oct. 1991.
[2] A.F. Benner, H.F. Jordan, and V.P. Heuring, "Digital Optical Computing with Optically Switched Directional Couplers," Optical Eng., vol. 30, pp. 1,936-1,941, Dec. 1991.
[3] S. Barua, "High-Speed Multiplier for Digital Signal Processing," Optical Eng., vol. 30, pp. 1,997-2,002, Dec. 1991.
[4] V.E. Benes, "On Rearrangeable Three-Stage Connecting Networks," The Bell System Technical J., vol. 41, pp. 14,81-1,492, May 1962.
[5] K.H. Brenner, A. Huang, and N. Streibl, "Digital Optical Computing with Symbolic Substitution," Applied Optics, vol. 25, pp. 3,054-3,060, 1986.
[6] K.H. Brenner, "New Implementation of Symbolic Substitution Logic," Applied Optics, vol. 25, pp. 3,061-3,064, 1986.
[7] K.H. Brenner, A.W. Lohmann, and T.M. Merklein, "Symbolic Substitution Implemented by Spatial Filtering Logic," Optical Eng., vol. 28, pp. 390-396, 1989.
[8] J.A. Gallian, Contemporary Abstract Algebra, second edition. D.C. Heath and Company, 1990.
[9] H.L. Garner, "The Residue Number System," IRE Trans. Electronic Computers, vol. 8, pp. 140-147, June 1959.
[10] P.S. Guilfoyle and W.J. Wiley, "Combinatorial Logic Based Digital Optical Computing Architectures," Applied Optics, vol. 27, pp. 1,661-1,673, 1988.
[11] H.S. Hinton, "Switching to Photonics," IEEE Spectrum, vol. 29, no. 2, pp. 42-45, Feb. 1992.
[12] H. Jeon, M.A.G. Abushagur, A.A. Sawchuk, and B.K. Jenkins, "Digital Optical Processor Based on Symbolic Substitution Using Holographic Matched Filtering," Applied Optics, vol. 29, pp. 2,113-2,125, 1990.
[13] M. Kondo et al., "Integrated Optical Switch Matrix for Single-Mode Fiber Networks," IEEE J. Quantum Electronics, vol. 18, pp. 1,759-1,765, Oct. 1982.
[14] C.-T. Lea, "Crossover Minimization in Directional-Coupler-Based Photonic Switching Systems," IEEE Trans. Comm., vol. 36, pp. 355-363, Mar. 1988.
[15] M.-B. Lin and A.Y. Oruç, "The Design of a Network-Based Arithmetic Processor," UMIACS-TR-91-141, CS-TR-2780, College Park, Md., Oct. 1991.
[16] M.-B. Lin, "Unified Algebraic Computations on Permutation Networks," PhD dissertation, EE Dept., Univ. of Maryland, College Park, 1992.
[17] M.-B. Lin and A.Y. Oruç, "A Fault-Tolerant Permutation Network Modulo Arithmetic Processor," IEEE Trans. VLSI Systems, vol. 2, pp. 312-319, Sept. 1994.
[18] M.-B. Lin and A.Y. Oruç, "Constant Time Inner Product and Matrix Computations on Permutation Network Processors," IEEE Trans. Computers, vol. 43, no. 12, pp. 1,429-1,434, Dec. 1994.
[19] A. Louri and A. Post, "Complexity Analysis of Optical-Computing Paradigms," Applied Optics, vol. 31, no. 26, pp. 5,568-5,583, Sept. 1992.
[20] A.D. McAulay, Optical Computer Architectures: The Application of Optical Concepts to Next Generation Computers. John Wiley and Sons, 1991.
[21] M.J. Murdocca, A. Huang, J. Jahns, and N. Streibl, "Optical Design of Programmable Logic Arrays," Applied Optics, vol. 27, pp. 1,651-1,660, 1988.
[22] M.J. Murdocca and T.J. Cloonan, "Optical Design of a Digital Switch," Applied Optics, vol. 28, pp. 2,505-2,517, 1989.
[23] W.K. Nicholson, Introduction to Abstract Algebra. PWS-KENT Publishing Company, 1993.
[24] J.P. Pratt and V.P. Heuring, "Designing Digital Optical Computing Systems: Power Distribution and Cross Talk," Applied Optics, vol. 31, pp. 4,657-4,661, Aug. 1992.
[25] H.E. Rose, A Course in Number Theory.New York: Oxford Univ. Press, 1988.
[26] A.S. Shenoy and R. Kumaresan, "Residue to Binary Conversion for RNS Arithmetic Using Only Modular Look-Up Tables," IEEE Trans. Circuits and Systems, vol. 35, no. 9, pp. 1,158-1,162, Sept. 1988.
[27] T. Stouraitis, S.W. Kim, and A. Skavantzos, "Full Adder-Based Arithmetic Units for Finite Integer Rings," IEEE Trans. Circuits and Systems—II, vol. 40, pp. 740-745, Nov. 1993.
[28] J. Tanida and Y. Ichioka, "Modular Components for an Optical Array Logic System," Applied Optics, vol. 26, pp. 3,954-3,960, 1987.
[29] W.A. Waksman,“A permutation network,” J. ACM, vol. 15, pp. 159-163, 1968.

Index Terms:
Directional coupler switch, modulo arithmetic, optical computing, permutation network, residue codes.
Ming-Bo Lin, A. Yavuz Oruç, "The Design of an Optoelectronic Arithmetic Processor Based on Permutation Networks," IEEE Transactions on Computers, vol. 46, no. 2, pp. 142-153, Feb. 1997, doi:10.1109/12.565589
Usage of this product signifies your acceptance of the Terms of Use.