Message faults are caused by network crowding and signal fading at high frequencies of 5G and 6G. Current error-detection and correction algorithms are computationally demanding, especially for new low-cost reduced-capability IoT devices. Disclosed are methods for (a) determining whether a message is faulted using a compact error-detection code, (b) localizing the most likely faulted message element(s) according to the waveform signal, and (c) determining the likely corrected version by back-calculating from the error-detection code. Other versions include testing various modulation substitutions for the most suspicious message elements, having the worst signal quality. The waveform parameters may include a deviation from an average amplitude, phase, frequency, or polarization, as well as an amount of amplitude variation and phase variation within the message element. Identification of the most likely faulted message elements may enable recovery of the message without a costly retransmission.