On a Class of Rearrangeable Switching Networks - Part II: Enumeration Studies and Fault Diagnosis

This part of the paper will cover some of the theoretical considerations related to the rearrangeable switching networks discussed in Part I. For the general (N X A r ) network with base-d structure, it is shown that it can indeed accommodate any of the N connection patterns. A thorough study is then made of the (N X A7) network having a base-2 structure. Tt was pointed out in Part I that the setting of the ^-element is, in general, not unique for an arbitrary input-output permutation. Furthermore, the number of /3-elements for an (N X N) network exceeds (logL. (A 7 !)), for N > 4. Some enumeration studies are given to account for this. Finally, fault diagnostic studies are given in relation to the base-2 network. A method to construct a set of permutations useful for testing the network is developed. This is then followed by discussing a procedure to detect and/or locate faulty /^-elements in the network. I I . PERMUTATION PROPERTY OF THE NETWORK In this section it will be shown that the decomposition of the given permutation into reducible connection sets fas used in the control 1601