Realization of large-scale distributors based on Batcher sorters

We rigorously examine how to construct a large-scale distributor by taking a logical and systematic approach. We first consider requirements for realization, which include the independent operation of unit modules and the packet sequence integrity, and consider what kind of existing devices have large-scale growth potential. In this process, we take the Batcher sorting network as the candidate device and show that the distribution function can be incorporated to it by furnishing each constituent sorting element with the state inversion capability. Then we show that this is equivalent to replacing each sorting element with a 2×2 distributor. As a consequence, the large-scale distributor design problem turns into a simple substitution problem for which we substitute a unit distributor for each sorting element in the prototype Batcher sorting network. In addition, we show that this substitution approach can be extended to larger scale unit distributor modules, thus enabling a large-scale distributor realization. The resulting large-scale distributor design procedure can be summarized as follows: given a desired size L=MN for the design of a large-scale distributor, we first design an N×N Batcher sorter (BS) and then replace each constituent 2×2 sorting element with a 2M×2M distributor module