A hidden semi-Markov QP-model is considered; and the way it could be embedded in a general hidden semi-Markov model is shown. The estimation problem (the first of three classical theory problems of the hidden Markov models and hidden semi-Markov models) is solved for the hidden semi-Markov QP-model. The solution is based on Shun-Zheng Yu forward algorithm for a general hidden semi-Markov model. This approach differs from the traditional one and employs posterior probabilities. The estimation problem solution of the hidden semi-Markov QP-model is an important step in solving the following more specific problem. That is the selection problem based on the recorded in the data channel model error sequence from the base of hidden semi-Markov QP-models that generates the closest to the channel sequence error streams. The fitting problem solution will make it possible to evaluate the correcting capability of the noise-free codec towards errors of various types, and to select the optimal codec for a particular communication channel on the basis of the computer simulation experiments.