Failure-correction decoding (FCD) is a decoding method that improves the performance of error-correction block codes by using reliability estimates of the received digit decisions. The FCD logic producesFfailures by erasing theFdigits of a received code character that are most probably in error. Since the numberFis the code's erasure-correction capability, the decoding is always possible and will yield a correct character if the failures include all errors. FCD operation is evaluated for short block codes and the Rayleigh-fading, the Gaussian-noise, and the atmospheric-noise channels. Significantly lower error probabilities, in comparison to error-correction decoding, are obtained for the Rayleigh-fading and the atmospheric-noise channels, but only minor improvement is obtained for the Gaussian-noise channel. The optimum failure-selection criterion for the fast Rayeligh-fading channel and noncoherent detection is to select as failures theFdigits with the least difference between the squared-envelope amplitudes from the two matched-filter outputs. For the atmospheric-noise channel, a good failure-selection criterion is to choose theFdigits with the largest noise-envelope amplitude as measured in an adjacent frequency band.