Parallel computing with optical interconnects

Optics has become an appealing alternative to wired interconnections on several levels of communication hierarchy within computing systems. Optical chip interconnections, unlike electrical, are insensitive to mutual interference effects, are free from capacitive loading and planar constraints, and can be reprogrammable. A major goal of this thesis is to understand the computational limits in using optical communication technology in VLSI parallel processing systems. Established methodologies for studying computational complexity are applied to obtain measures that reflect true implementation costs. The computational lower founds derived using the VLSI model of computation indicate that solution to communication-intensive problems requires either a large amount of chip area or time, both of which are costly. The first part of the thesis introduces an Optical Model of Computation (OMC) that uses free space optics as a means of interprocessor communication; thus reducing chip costs. The model allows unit cost communications, and can efficiently simulate PRAM. Since OMC uses the space above and around chips for interconnects, OMC can be compared with three dimensional VLSI models in computational complexity. Any computation performed by a three dimensional VLSI organization having N processors with degree d, in time T, and volume V can be performed on OMC in volume v, and time t, where dT/N $\leq$ t $\leq$ T, and Nd $\leq$ v. The thesis presents various parallel architectures as possible efficient upper bounds for v. Each one is designed to reflect the capabilities and limitations of the device technologies used for the redirection of optical beams. Having developed the computational models, the thesis next focuses on applications in image processing and the implementation of AI problem solving techniques. A set of O(log N) pointer based algorithms for finding geometric properties of digitized images on an electro-optical mesh is introduced. The algorithms include optimal solutions for identifying and labeling figures, computing convexity properties, determining distances, etc. Another application is in the implementation of neural networks using a general purpose electro-optical cross-bar which has the potential to interconnect each of the neurons to all the others. This architecture can be modified to operate asynchronously and to realize the data-flow model.

[1]  B. Keith Jenkins.  Architectural Characteristics of Optical Logic Systems , 1985, COMPCON.

[2]  A A Sawchuk,et al.  Optical crossbar interconnections using variable grating mode devices. , 1987, Applied optics.

[3]  V. K. Prasanna Kumar,et al.  Communication complexity of various vlsi models , 1983 .

[4]  R. Hecht-Nielsen,et al.  Neurocomputing: picking the human brain , 1988, IEEE Spectrum.

[5]  Russ Miller,et al.  Geometric Algorithms for Digitized Pictures on a Mesh-Connected Computer , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Dennis G. Hall.  Survey of Silicon-Based Integrated Optics , 1987, Computer.

[7]  Michael J. Quinn,et al.  Designing Efficient Algorithms for Parallel Computers , 1987 .

[8]  C. Lee Giles,et al.  Parallel Processing Paradigms And Optical Computing , 1986, Photonics West - Lasers and Applications in Science and Engineering.

[9]  Viktor K. Prasanna,et al.  Array Processor with Multiple Broadcasting , 1985, ISCA.

[10]  Insup Lee,et al.  Synthesis and Mapping Algorithms for a Reconfigurable Optical Interconnection Network , 1986, ICPP.

[11]  Jeffrey D Ullma.  Computational Aspects of VLSI , 1984 .

[12]  A. Mullin,et al.  Mathematical Theory of Connecting Networks and Telephone Traffic. , 1966 .

[13]  Kenneth D. Pedrotti,et al.  Optoelectronic Integrated Circuits For High Speed Signal Processing , 1986 .

[14]  Dionysios I. Reisis,et al.  Data Movement Operations and Applications on Reconfigurable VLSI Arrays , 1988, ICPP.

[15]  Richard P. Hopkins,et al.  Data-Driven and Demand-Driven Computer Architecture , 1982, CSUR.

[16]  Howard Jay Siegel,et al.  Interconnection networks for large-scale parallel processing: theory and case studies (2nd ed.) , 1985 .

[17]  Francesco Romani,et al.  A compact and modular VLSI design for the solution of general sparse linear systems , 1987, Integr..

[18]  Pierre Gidon,et al.  Integrated Optics On Silicon Substrate : A Way To Achieve Complex Optical Circuits , 1986, Other Conferences.

[19]  Steven L. Tanimoto,et al.  A pyramidal approach to parallel processing , 1983, ISCA '83.

[20]  Carver A. Mead,et al.  VLSI architectures for implementation of neural networks , 1987 .

[21]  H. Kogelnik.  Limits in integrated optics , 1981, Proceedings of the IEEE.

[22]  Demetri Psaltis,et al.  Shift-Invariant Optical Associative Memories , 1987 .

[23]  Eli Upfal,et al.  Efficient schemes for parallel communication , 1982, PODC '82.

[24]  Davis H. Hartman,et al.  Digital High Speed Interconnects: A Study Of The Optical Alternative , 1986 .

[25]  Joseph W. Goodman,et al.  Optical Clock Distribution To Silicon Chips , 1986 .

[26]  S. Valette,et al.  Integrated Fresnel lens on thermally oxidized silicon substrate. , 1981, Applied optics.

[27]  Azriel Rosenfeld,et al.  Digital Picture Processing , 1976 .

[28]  Mark H. Overmars,et al.  Notes on maintenance of configurations in the plane , 1980 .

[29]  R. S. Withers,et al.  An artificial neural network integrated circuit based on MNOS/CCD principles , 1987 .

[30]  D. L. Smythe,et al.  A Technology For Optical Interconnections Based On Multichip Integration , 1986 .

[31]  Charles L. Seitz,et al.  Engineering limits on computer performance , 1984 .

[32]  J. Fried.  Optical I/O For High Speed CMOS Systems , 1986 .

[33]  F. Morehead.  Light-Emitting Semiconductors , 1967 .

[34]  Erik I. Verriest,et al.  Matrix Triangularization Using Arrays of Integrated Optical Givens Rotation Devices , 1987, Computer.

[35]  Tse-yun Feng,et al.  A Survey of Interconnection Networks , 1981, Computer.

[36]  C. Lee Giles,et al.  Superposition In Optical Computing , 1989, Other Conferences.

[37]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[38]  David Casasent.  Guidelines For Efficient Use Of Optical Systolic Array Processors , 1983, Other Conferences.

[39]  S. Teng,et al.  Optimal Tree Contraction in the EREW Model , 1988 .

[40]  J. Hopfield,et al.  Computing with neural circuits: a model. , 1986, Science.

[41]  B K Jenkins,et al.  Architectural implications of a digital optical processor. , 1984, Applied optics.

[42]  Mehrnoosh M. Eshaghian,et al.  Massively Parallel Architectures With Optical Interconnection Networks , 1989, Other Conferences.

[43]  M. F.,et al.  Bibliography , 1985, Experimental Gerontology.

[44]  C. Thomborson,et al.  Area-time complexity for VLSI , 1979, STOC.

[45]  Pierre Gidon,et al.  Optical Interconnections For WSI , 1989, Other Conferences.

[46]  Pierre Gidon,et al.  Integrated Lenses On Silicon Nitride Waveguides , 1985 .

[47]  H. M. Alnuweiri,et al.  Optimal image computations on reduced VLSI architectures , 1989 .

[48]  Lawrence D. Jackel,et al.  VLSI implementation of a neural network memory with several hundreds of neurons , 1987 .

[49]  P. W. Smith.  Digital Optics: Progress Towards Practical Applications , 1987, Other Conferences.

[50]  B. K. Jenkins,et al.  Computer-Generated Holograms For Space-Variant Interconnections In Optical Logic Systems , 1983, Optics & Photonics.

[51]  Larry A. Bergman,et al.  Holographic optical interconnects for VLSI , 1986 .

[52]  Ho-In Jeon,et al.  Digital optical processor based on symbolic substitution using holographic matched filtering. , 1990, Applied optics.

[53]  Charles E. Leiserson,et al.  Randomized Routing on Fat-Trees , 1989, Adv. Comput. Res..

[54]  D. J. Evans.  Sparsity and its applications , 1986 .

[55]  Herbert Freeman,et al.  Determining the minimum-area encasing rectangle for an arbitrary closed curve , 1975, CACM.

[56]  Paul R. Prucnal,et al.  VLSI Fiber Optic Local Area Network , 1987, Other Conferences.

[57]  Francis Arthur Jenkins,et al.  Fundamentals of Optics , 1976 .

[58]  A. Huang,et al.  Architectural considerations involved in the design of an optical digital computer , 1984, Proceedings of the IEEE.

[59]  Arvind,et al.  A Computer Capable of Exchanging Processors for Time , 1977, IFIP Congress.

[60]  J Shamir,et al.  Massive holographic interconnection networks and their limitations. , 1989, Applied optics.

[61]  C. Thomborson,et al.  A Complexity Theory for VLSI , 1980 .

[62]  Kai Hwang,et al.  Computer architecture and parallel processing , 1984, McGraw-Hill Series in computer organization and architecture.

[63]  Cauligi S. Raghavendra,et al.  Optical Crossbar Networks , 1987, Computer.

[64]  Viktor K. Prasanna,et al.  Parallel Geometric Algorithms for Digitized Pictures on Mesh of Trees , 1986, ICPP.

[65]  Sartaj Sahni,et al.  Parallel Algorithms to Set Up the Benes Permutation Network , 1982, IEEE Transactions on Computers.

[66]  David Casasent.  "Optical Artificial Intelligence Processors" , 1987, Other Conferences.

[67]  Ajit Agrawal,et al.  A Parallel O(log N) Algorithm for Finding Connected Components In Planar Images , 1987, ICPP.

[68]  D Psaltis,et al.  Optical information processing based on an associative-memory model of neural nets with thresholding and feedback. , 1985, Optics letters.

[69]  Richard Cole,et al.  Optimal Parallel Algorithms for Expression Tree Evaluation and List Ranking , 1988, AWOC.

[70]  Robert Hecht-Nielsen,et al.  Performance Limits Of Optical, Electro-Optical, And Electronic Neurocomputers , 1986, Other Conferences.

[71]  Azriel Rosenfeld.  The prism machine: An alternative to the pyramid , 1985, J. Parallel Distributed Comput..

[72]  Demetri Psaltis.  Optical Realizations Of Neural Network Models , 1987, Other Conferences.

[73]  E. Marom,et al.  Programmable Optical Interconnects , 1987, Other Conferences.

[74]  Satoshi Fujita,et al.  A template matching algorithm using optically-connected 3-D VLSI architecture , 1987, ISCA '87.

[75]  James J. Sluss,et al.  An Introduction to Integrated Optics for Computing , 1987, Computer.

[76]  Ronald L. Rivest,et al.  The Design and Analysis of Computer Algorithms , 1990 .

[77]  Demetri Psaltis,et al.  Higher order associative memories and their optical implementations , 1988, Neural Networks.

[78]  Howard Jay Siegel,et al.  Parallel Processing Approaches to Image Correlation , 1982, IEEE Transactions on Computers.

[79]  R Barakat,et al.  Lower bounds on the computational efficiency of optical computing systems. , 1987, Applied optics.

[80]  S. N. Maheshwari,et al.  Efficient VLSI Networks for Parallel Processing Based on Orthogonal Trees , 1983, IEEE Transactions on Computers.

[81]  Russ Miller,et al.  Convexity algorithms for pyramid computers , 1984 .

[82]  Mark A. Bobb.  Laser Diode Collimators For Free Space Optical Communications , 1987, Photonics West - Lasers and Applications in Science and Engineering.