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Motivated by the inherent correlation between the speech features and their lexical words, we propose in this paper a new framework for learning the parameters of the corresponding acoustic and language models jointly. The proposed framework is based on discriminative training of the models' parameters using minimum classification error criterion. To verify the effectiveness of the proposed framework, a set of four large decoding graphs is constructed using weighted finite-state transducers as a composition of two sets of context-dependent acoustic models and two sets of n-gram-based language models. The experimental results conducted on this set of decoding graphs validated the effectiveness of the proposed framework when compared with four baseline systems based on maximum likelihood estimation and separate discriminative training of acoustic and language models in benchmark testing of two speech corpora, namely TIMIT and RM1.