Pseudo-Random Sequences with a Priori Distribution

Abstract

This paper introduces a hypergraph-theoretic technique for the synthesis of sequences with prescribed distributions. A positive n-distribution is an assignment of a positive integer to each n-letter word with letters chosen from some fixed finite alphabet. A distribution is atomic if it always assigns the same integer to words that are cyclic shifts of each other. A periodic sequence of letters from the alphabet is said to realize a given distribution if the distribution assigns to each word its frequency of occurrence in a single period of the sequence. Given a positive atomic redistribution, we construct a hypergraph, the subgraphs of which correspond to a family of modified nonlinear feedback shift registers. Each shift register in a family corresponding to a spanning hypertree of the hypergraph will generate a sequence realizing the given distribution.

This research was accomplished as part of the MITRE Corporation’s Independent Research and Development Program.