ON AN APPROXIMATE EIGENVECTOR ASSOCIATED WITH A MODULATION CODE

Let S be a constrained system of finite type, described in terms of a labeled graph M of finite type. Furthermore, let C be an irreducible c onstrained system of finite type, consisting of the collection of poss ible code sequences of some finite-state-encodable, sliding-block-deco dable modulation code for S. It is known that this code could then be obtained by state splitting, using a suitable approximate eigenvector. In this correspondence, we show that the collection of all approximat e eigenvectors that could be used in such a construction of C contains a unique minimal element. Moreover, we show how to construct its line ar span from knowledge of M and C only, thus providing a lower bound o n the components of such vectors. For illustration we discuss an examp le showing that sometimes arbitrary large approximate eigenvectors are required to obtain the best code (in terms of decoding-window size) a lthough a small vector is also available.