Dealing with short cycles in graphical codes

The graphical representation of codes has opened the way to soft decoding by belief propagation, which extends the usual soft Viterbi decoding. This simple algorithm is most often used for constructing and evaluating graphical codes. We show that belief propagation on graphs is not always appropriate and that the algorithmic resources for graphical models are far more extended than belief propagation. In particular, we propose new approximate decoders based on the “conditioning technique” to solve the short cycles problem of graphical codes