1993
DOI: 10.1364/ao.32.004992
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Basic building blocks for the switch-preserving transformation of shuffle interconnections

Abstract: The transformations of a two-dimensional shuffle on a 4 × 4 array into a one-dimensional shuffle on a vector of length 16 (and vice versa) are recognized as basic building blocks for the switch-preserving transformation of shuffle patterns of any size. [The switch-preserving transformation means the transformation of one-dimensional shuffles into two-dimensional and d-dimensional shuffles (d ≥ 3) and vice versa without the subdivision of switches.] The switch-preserving transformation of shuffle patterns on la… Show more

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Cited by 7 publications
(6 citation statements)
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“…We found six different TPs through 4x4-arrays which all are capable to transform the 1-D shuffle S(4,4) into the 2-D shuffle S2_D(2, 2; 2, 2) and vice versa [1]. The TPs#1 and #2 in Fig.…”
Section: Different Tpsmentioning
confidence: 92%
See 2 more Smart Citations
“…We found six different TPs through 4x4-arrays which all are capable to transform the 1-D shuffle S(4,4) into the 2-D shuffle S2_D(2, 2; 2, 2) and vice versa [1]. The TPs#1 and #2 in Fig.…”
Section: Different Tpsmentioning
confidence: 92%
“…1 For symmetric 2-D shuffles (symmetric decomposition of coordinates, e.g. 8=2x4 or =4x2, 16=4x4 or =2x8 or =8x2 at both coordinates) defined on squares, TPs always exist and may be obtained geometrically [1]. In particular, in this case, TPs may be defined recursively, i.e.…”
Section: Conceptmentioning
confidence: 99%
See 1 more Smart Citation
“…Equation (21) has been derived by expressing the maximum skew of the KPS (Appendix A). The maximum number of crossed channels is twice the results for KPS (22) and the structure of (19) remains valid.…”
Section: Distributed Switchesmentioning
confidence: 99%
“…The implementation of interconnections in space and frequency is a challenge for the current photonic technology as well as it raises several questions which have to be answered by the photonic system research. For example, in order to mention a few of them, the proper balance *Manuscript received January 21,1993. The author is with Heinrich-Hertz-Institut fiir Nachrichtentechnik Berlin GmbH, Einsteinufer 37, D-10587 Berlin, Federal Republic of Germany.…”
Section: Introductionmentioning
confidence: 99%