This work aims at bridging the gap between two completely distinct research fields: digital communications and Music Information Retrieval. While works in the MIR community have long used algorithms borrowed from speech signal processing, text recognition or image processing, to our knowledge very scarce work based on digital communications algorithms has been produced. This paper specifically targets the use of the Belief Propagation algorithm for the task of Automatic Chord Estimation. This algorithm is of widespread use in iterative decoders for error correcting codes and we show that it offers improved performances in ACE by genuinely incorporating the ability to take constraints between distant parts of the song into account. It certainly represents a promising alternative to traditional MIR graphical models approaches, in particular Hidden Markov Models.