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In analyses of the convolutional codes with soft decision Viterbi decoding, an upper bound approach was widely adopted to evaluate the error performance. The upper bound approach gives better estimation of error performance in high signal-to-noise-power ratio (SNR) condition, by contrast, it gives a poor result in low SNR. The exact bit error analyses of convolutional codes have been reported. Their method can derive exact error performance in low SNR. Besides, they employ an iterative calculation of probability density function (pdf) without considering truncation errors. The purpose of this paper is to extend their result to the error performance with truncation errors due to a finite path history. Furthermore, an application to the interference channels is demonstrated.