Extensions of the Method of Poles for Code Construction

The method of poles is a method introduced by P. A. Franaszek for constructing a rate 1 : 1 nite state code from k-ary data into a constrained channel S, where S is recognized by a given local automaton and S has a capacity greater than log(k). The method is based on the computation of a set of states that we call poles. To each pole is associated a set of paths going from this pole to others. The code produced by the method of poles has a sliding block decoder if each set of paths satisses the following optimization condition: the sum of the path lengths is minimal among all other possible sets. In this paper we give a better optimization condition to get the sliding block window decoding property, and we extend the method to the more general case of sooc constrained channels.