The invention is a way to detect and correct data inversions or other phase ambiguities in a modem's data, without incurring a significant penalty in error rate performance, throughput, or overhead, by making a particular use of the error detection and correction (EDAC) code which would typically be used for random errors. The decoder is set up so that the inverted data or out-of-phase data generates a distinctive syndrome which signals to a phase corrector.