A pipelined single-bit controlled sorting network with O(Nlog2 N) bit complexity

We propose a pipelined optical sorting network to sort N w-bit inputs using O(wNlogN) single bit-controlled 2×2 switching elements. The network is compared to the standard Batcher (1968) sorter which requires (O(Nlog²N)) two-input comparators for sorting N log N-bit words. However each comparator in the Batcher sorter has to perform a word comparison between two log N bit inputs, as opposed to single-bit controlled switching elements in the proposed scheme. An alternative implementation of the proposed network maintains the same hardware complexity while showing an O(loglogN) improvement in latency over the Batcher sorter. The proposed network is based on binary radix sort and utilizes a pair of self-routing reverse banyan networks to implement each step of the radix-sort algorithm. A distributed single-bit control scheme due to a particular non-blocking property of the reverse banyan network is used to route packets through each reverse banyan. Given the high cost of optical switches, the low hardware and control complexity of the network makes it easy to replace electronic switching elements with 2×2 lithium niobate directional couplers, thus making the network attractive for high-speed optical applications