An iterative matrix-based procedure for finding the shannon cover for constrained sequences

Abstract

In many applications such as coding for magnetic and optical recording, the determination of the graph with the fewest vertices (i.e., the Shannon cover) presenting a given set of constrained sequences (i.e., shift of finite type) is very important. The main contribution of this paper is an efficient iterative vertex-minimization algorithm, which manipulates the symbolic adjacency matrix associated with an initial graph presenting a shift of finite type. A characterization of this initial graph is given. By using the matrix representation, the minimization procedure to finding the Shannon cover becomes easy to implement using a symbolic manipulation program, such as Maple. © Springer-Verlag 2004.