Extensions of the method of poles for code construction

The method of poles is a method introduced by Franaszek (1969) for constructing a rate-1:1 finite-state code from k-ary data into a constrained channel of finite type whose capacity is strictly greater than log(k). The method is based on the computation of a set of states called poles. With each pole is associated a set of paths going from this pole to others. Each set verifies an entropy condition. The code produced by the method of poles has a sliding-block decoder if each set of paths satisfies moreover an optimization condition based on the sum of the path lengths of the set. We give a new optimization condition which guarantees the sliding-block window decoding property and has a lower computational complexity than the previous one. We also extend the method of poles to the more general case of sofic constrained channels.