Abstract

The concept of a perfect shuffle is reviewed. Holographic approaches based on implementing a point spread function equivalent to the sum of two shifted delta functions are suggested. Interferometric approaches based on splitting an image and then combining them in a shifted manner are also suggested.

© 1988 Optical Society of America

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References

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  1. H. S. Stone, “Parallel Processing with the Perfect Shuffle,” IEEE Trans. Comput. C-20, 153 (1971).
    [CrossRef]
  2. C. L. Wu, T. Y. Feng, “The Universality of the Shuffle-Exchange Network,” IEEE Trans. Comput. C-30, 324 (1981).
    [CrossRef]
  3. V. Benes, Mathematical Theory of Connecting Networks (Academic, New York, 1965).
  4. K. E. Batcher “Sorting Networks, and their Applications,” in Proceedings, AFIPS 1968 SJCC, 32, No. 2 (AFIPS Press, Montvale, NJ, 1968), pp. 307.
  5. J. H. Patel, “Processor-Memory Interconnections for Multiprocessors,” in Proceedings, Sixth Annual Symposium on Computer Architecture, New York, (Apr.1979), pp. 168.
    [CrossRef]
  6. T. Lang, H. S. Stone, “A Shuffle-Exchange Network with Simplified Control, IEEE Trans. Comput. C-25, 55 (1976).
    [CrossRef]
  7. D. Nassimi, S. Sahni, “A Self-Routing Benes Network and Parallel Permutation Algorithms,” IEEE Trans. Comput. C-30, 332 (1981).
    [CrossRef]
  8. A. Huang, S. Knauer, J. O’Neill, “Case Study: A Self-Routing Switching Network,” in Principles of CMOS VLSI Design—A Systems Perspective, Neil Weste, Ed. (Addison-Wesley, Reading, MA, 1985).
  9. A. Huang, S. Knauer, “STARLITE: a Wideband Digital Switch,” in Conference Proceedings, GLOBECOM ’84, IEEE 84CH2064-4, Vol. 1, Nov.1984, pp. 121–125.
  10. J. W. Goodman, F. I. Leonberger, S.-Y. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc., IEEE 72, 850 (1984).
    [CrossRef]

1984 (1)

J. W. Goodman, F. I. Leonberger, S.-Y. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc., IEEE 72, 850 (1984).
[CrossRef]

1981 (2)

C. L. Wu, T. Y. Feng, “The Universality of the Shuffle-Exchange Network,” IEEE Trans. Comput. C-30, 324 (1981).
[CrossRef]

D. Nassimi, S. Sahni, “A Self-Routing Benes Network and Parallel Permutation Algorithms,” IEEE Trans. Comput. C-30, 332 (1981).
[CrossRef]

1976 (1)

T. Lang, H. S. Stone, “A Shuffle-Exchange Network with Simplified Control, IEEE Trans. Comput. C-25, 55 (1976).
[CrossRef]

1971 (1)

H. S. Stone, “Parallel Processing with the Perfect Shuffle,” IEEE Trans. Comput. C-20, 153 (1971).
[CrossRef]

Athale, R. A.

J. W. Goodman, F. I. Leonberger, S.-Y. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc., IEEE 72, 850 (1984).
[CrossRef]

Batcher, K. E.

K. E. Batcher “Sorting Networks, and their Applications,” in Proceedings, AFIPS 1968 SJCC, 32, No. 2 (AFIPS Press, Montvale, NJ, 1968), pp. 307.

Benes, V.

V. Benes, Mathematical Theory of Connecting Networks (Academic, New York, 1965).

Feng, T. Y.

C. L. Wu, T. Y. Feng, “The Universality of the Shuffle-Exchange Network,” IEEE Trans. Comput. C-30, 324 (1981).
[CrossRef]

Goodman, J. W.

J. W. Goodman, F. I. Leonberger, S.-Y. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc., IEEE 72, 850 (1984).
[CrossRef]

Huang, A.

A. Huang, S. Knauer, “STARLITE: a Wideband Digital Switch,” in Conference Proceedings, GLOBECOM ’84, IEEE 84CH2064-4, Vol. 1, Nov.1984, pp. 121–125.

A. Huang, S. Knauer, J. O’Neill, “Case Study: A Self-Routing Switching Network,” in Principles of CMOS VLSI Design—A Systems Perspective, Neil Weste, Ed. (Addison-Wesley, Reading, MA, 1985).

Knauer, S.

A. Huang, S. Knauer, J. O’Neill, “Case Study: A Self-Routing Switching Network,” in Principles of CMOS VLSI Design—A Systems Perspective, Neil Weste, Ed. (Addison-Wesley, Reading, MA, 1985).

A. Huang, S. Knauer, “STARLITE: a Wideband Digital Switch,” in Conference Proceedings, GLOBECOM ’84, IEEE 84CH2064-4, Vol. 1, Nov.1984, pp. 121–125.

Kung, S.-Y.

J. W. Goodman, F. I. Leonberger, S.-Y. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc., IEEE 72, 850 (1984).
[CrossRef]

Lang, T.

T. Lang, H. S. Stone, “A Shuffle-Exchange Network with Simplified Control, IEEE Trans. Comput. C-25, 55 (1976).
[CrossRef]

Leonberger, F. I.

J. W. Goodman, F. I. Leonberger, S.-Y. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc., IEEE 72, 850 (1984).
[CrossRef]

Nassimi, D.

D. Nassimi, S. Sahni, “A Self-Routing Benes Network and Parallel Permutation Algorithms,” IEEE Trans. Comput. C-30, 332 (1981).
[CrossRef]

O’Neill, J.

A. Huang, S. Knauer, J. O’Neill, “Case Study: A Self-Routing Switching Network,” in Principles of CMOS VLSI Design—A Systems Perspective, Neil Weste, Ed. (Addison-Wesley, Reading, MA, 1985).

Patel, J. H.

J. H. Patel, “Processor-Memory Interconnections for Multiprocessors,” in Proceedings, Sixth Annual Symposium on Computer Architecture, New York, (Apr.1979), pp. 168.
[CrossRef]

Sahni, S.

D. Nassimi, S. Sahni, “A Self-Routing Benes Network and Parallel Permutation Algorithms,” IEEE Trans. Comput. C-30, 332 (1981).
[CrossRef]

Stone, H. S.

T. Lang, H. S. Stone, “A Shuffle-Exchange Network with Simplified Control, IEEE Trans. Comput. C-25, 55 (1976).
[CrossRef]

H. S. Stone, “Parallel Processing with the Perfect Shuffle,” IEEE Trans. Comput. C-20, 153 (1971).
[CrossRef]

Wu, C. L.

C. L. Wu, T. Y. Feng, “The Universality of the Shuffle-Exchange Network,” IEEE Trans. Comput. C-30, 324 (1981).
[CrossRef]

IEEE Trans. Comput. (4)

H. S. Stone, “Parallel Processing with the Perfect Shuffle,” IEEE Trans. Comput. C-20, 153 (1971).
[CrossRef]

C. L. Wu, T. Y. Feng, “The Universality of the Shuffle-Exchange Network,” IEEE Trans. Comput. C-30, 324 (1981).
[CrossRef]

T. Lang, H. S. Stone, “A Shuffle-Exchange Network with Simplified Control, IEEE Trans. Comput. C-25, 55 (1976).
[CrossRef]

D. Nassimi, S. Sahni, “A Self-Routing Benes Network and Parallel Permutation Algorithms,” IEEE Trans. Comput. C-30, 332 (1981).
[CrossRef]

Proc., IEEE (1)

J. W. Goodman, F. I. Leonberger, S.-Y. Kung, R. A. Athale, “Optical Interconnections for VLSI Systems,” Proc., IEEE 72, 850 (1984).
[CrossRef]

Other (5)

A. Huang, S. Knauer, J. O’Neill, “Case Study: A Self-Routing Switching Network,” in Principles of CMOS VLSI Design—A Systems Perspective, Neil Weste, Ed. (Addison-Wesley, Reading, MA, 1985).

A. Huang, S. Knauer, “STARLITE: a Wideband Digital Switch,” in Conference Proceedings, GLOBECOM ’84, IEEE 84CH2064-4, Vol. 1, Nov.1984, pp. 121–125.

V. Benes, Mathematical Theory of Connecting Networks (Academic, New York, 1965).

K. E. Batcher “Sorting Networks, and their Applications,” in Proceedings, AFIPS 1968 SJCC, 32, No. 2 (AFIPS Press, Montvale, NJ, 1968), pp. 307.

J. H. Patel, “Processor-Memory Interconnections for Multiprocessors,” in Proceedings, Sixth Annual Symposium on Computer Architecture, New York, (Apr.1979), pp. 168.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Perfect shuffle permutation of eight inputs.

Fig. 2
Fig. 2

Perfect shuffle implemented via interlacing two images.

Fig. 3
Fig. 3

Perfect shuffle implemented via a Michelson arrangement.

Fig. 4
Fig. 4

Perfect shuffle implemented via a Mach-Zehnder arrangement.

Fig. 5
Fig. 5

Perfect shuffle implemented via a Sagnac arrangement.

Fig. 6
Fig. 6

Constant latency optical perfect shuffle.

Equations (2)

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k = { 2 k if 0 k < N / 2 , 2 k N + 1 if N / 2 k < N .
p ˜ ( x ) = cos ( 2 π δ x λ f x ) .

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