A Generalization of Girod's Bidirectional Decoding Method to Codes with a Finite Deciphering Delay

In this paper we generalize an encoding method due to Girod (cf. [7]), based on binary prefix codes, that allows a bidirectional decoding of the encoded messages. In particular we generalize it to any finite alphabet A, to any operation defined on A, to any code with finite deciphering delay and to any key x ∈ A∗, whose length depends on the deciphering delay. We moreover define, as in [5], a deterministic transducer for such generalized method. We prove that, for a fixed code X over a given alphabet A with finite deciphering delay and for a fixed key x ∈ A∗, the transducers associated to different operations are isomorphic as unlabelled graphs. As an important result we moreover prove that, for a fixed code X ⊂ A with finite deciphering delay, transducers associated to different keys have an isomorphic non trivial strongly connected component.