A solution to the problem of speech recognition with signals distorted by low-bit rate coders is presented in this paper. A model for the coding-decoding distortion, a HMM compensation method to include this model, and an EM-based adaptation algorithm to estimate this distortion are proposed here. Medium vocabulary continuous-speech speaker-independent recognition experiments with 8 kbps G.729(CS-CELP), 13 kbps RPE-LTP (GSM), 5.3 kbps G723.1, 4.8 kbps FS-1016 and 32 kbps G.726(ADPCM) coders show that the approach described in this paper is able to dramatically reduce the effect of the coding distortion and, in some cases, gives a word accuracy higher than the baseline system with uncoded speech. Finally, the EM estimation algorithm requires only one adapting utterance and the approach described is certainly The evolution and popularity of cellular and TCP/IP networks has created the problem of improving the recognition accuracy for speech distorted by low-bit rate coders. The distortion of coding schemes in speech recognizers is difficult to model and is an open problem that cannot be solved by applying conventional noise cancelling techniques [1] such as spectral subtraction [2], cepstral mean subtraction [3] and RASTA