Recently, the first version of an ETSI standard for Distributed Speech Recognition has been proposed. The main benefit of this approach is the possibility of maintaining a high recognition performance when accessing remote information systems. The use of a digital channel for transmission of the encoded speech parameters implies the introduction of several channel distortions. Our paper deals with the mitigation of such distortions. We study the application of MMSE estimation to this problem and propose a new MMSE procedure that obtains the probabilities needed for MMSE from a forward-backward algorithm. We show that MMSE estimation obtains better performance than the mitigation algorithm described in the ETSI standard under different channel conditions.