A Table Look Up Approach to Loop Switching
L. H. Brandenburg, B. Gopinath · Bell System Technical Journal · 1972
In this paper we consider some questions of implementation of a scheme described in Section V of Ref. 1 for addressing message blocks in the Pierce loop system.2The scheme consists of using a stream of binary digits (0 and 1) as the address of the destination loop of a message such that the scalar product∗of the address with a stream of binary digits of equal length stored at a loop gives the distance between the loop and the destination. The message is routed along a path that minimizes distance between source and destination. The binary streams used in this scheme can be obtained by factoring the distance matrix D of the graph representing the connection of loops into two binary-valued matrices P and Q such that$D = PQ^{t},$where the superscript “t” stands for matrix transposition. The fcth row of P represents the address to be prefixed to a message destined for loop k. The fcth row of Q represents a binary sequence to be stored in loop k. The scheme discussed in Section V of Ref. 1 provides a particular way of factoring D. For completeness, we give a description of that factorization as follows.