A code to be decoded by message-passing is represented by a factor graph. The factor graph includes variable nodes indexed by i and constraint nodes indexed by a connected by edges for transferring messages mi→a outgoing from the variable nodes to the constraint nodes and messages ma→i incoming from the constraint nodes to the variable nodes. The messages mi→a are initialized based on beliefs bi of a received codeword. The messages ma→i are generated by overshooting the messages mi→a at the constraint nodes. The beliefs bi are updated at the variable nodes using the messages ma→i. The codeword is outputted if found, otherwise, the messages mi→a are updated using a correction for the overshooting.