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The classical method for decoding turbo codes is the Bahl-Cocke-Jelinek-Raviv (1974) algorithm which, in the majority of existing papers, is analyzed under the assumption of perfect channel knowledge and synchronization. In reality, however, its properties change significantly when synchronization is not ideal. We show that the influence of timing synchronization offset can be modeled as a decreased effective signal-to-noise ratio, which provides results consistent with simulations. Furthermore, we present a general model for the soft bit output of the BCJR algorithm and apply it to the situation when the received signal is sampled with a timing offset. Finally, we use the derived properties of the algorithm in a simple timing synchronizer which is shown to outperform the classical maximum-likelihood non-data-aided symbol synchronizer without a need of using additional pilot symbols.