Summary
Introduced by Lawrie, the Omega network is a powerful device to connect processing elements in a SIMD computer or in a multiprocessor architecture. Unfortunately it is not rearrangeable and some permutations that are frequently used to align data in a SIMD computer cannot be performed in one pass. Such is the case with the class of permutations induced by a permutation of index digits (PIPID) which includes the perfect shuffle, the bit reversal, etc. ... Using the techniques of linear algebra over the two-element field, we show that PIPIDs can be achieved by the Omega network through which the vector of data is routed twice.
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Lenfant, J., Tahé, S. Permuting data with the Omega network. Acta Informatica 21, 629–641 (1985). https://doi.org/10.1007/BF00289714
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DOI: https://doi.org/10.1007/BF00289714