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

Abstract

In this paper we generalize an encoding method due to Girod (cf. [6]) using 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 ⁺, on a length depending on the deciphering delay. We moreover define, as in [4], a deterministic transducer for such generalized method. We prove that, fixed a code X ∈ A ^* with finite deciphering delay and a key x ∈ A ^*, the transducers associated to different operations are isomorphic as unlabelled graphs. We also prove that, for a fixed code X with finite deciphering delay, transducers associated to different keys have an isomorphic non trivial strongly connected component.