A method for receiving an ADS-B message is disclosed including a synchronisation phase for detecting the start of the message and a decoding phase for recovering a bit stream corresponding to a block of data in the message. The synchronisation phase is based on determining a sequence of log-likelihood ratios having the greatest likelihood of corresponding to a sequence of symbols expected from a preamble of the message. Each log-likelihood ratio corresponds to a ratio between the respective probabilities that a symbol of the signal received corresponds to one of two possible values for a symbol. The decoding phase applies a belief propagation algorithm to a sequence of log-likelihood ratios respectively associated with the symbols in the block of data in the message, with an optimised parity matrix of the cyclic redundancy code of the message.