Arbitrary-size permutation networks using arbitrary-radix switches.

Permutation networks accepting an arbitrary number of inputs using arbitrary-radix switches find their applications in a wide range of areas such as datacenter network, network on chip, and network switches. We extend the Benes network to accepting an arbitrary-size input and using arbitrary-radix switches. The resulting network, namely A2-Benes network, has a regular topology as the Benes or Clos network while using fewer switches. For arbitrary n≥1 and w≥2, the number of switches of the n×n A2-Benes network is the total number of 1's and 0's in the radix-w representations of integers 0,…,n−1, not counting the leading 0's; the number of stages is 2⌈logw⁡n⌉−1. The regular topology and fewer switches of the A2-Benes network lead to lower wiring complexity and costs.