A x network, which is a concatenation of 2 Ω networks , along with a simple control algorithm is proposed. This network is capable of performing all Ω network realizable permutations and the bit-permute-complement (BPC) class of permutations  in O(log N) time. The control algorithm is actually a multiple-pass control algorithm on the Ω network, which is more general than Pease's LU decomposition method  and Lenfant's decomposition method .
- Bit-permute-complement permutations
- decomposition algorithms
- multiple-pass control algorithm
- network partitions
- Ω network