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Serial concatenation of convolutional codes and MSK through an interleaver has a similar structure as turbo codes. Although the union bound, which is an analytical tool to estimate the bit error probability of such systems, is tight for high signal-to-noise ratio (SNR), it diverges for low SNR where the performance of our system is the most appealing. For this reason, we apply improved upper bounding techniques to our system to estimate the performance, at low SNR. We show that by applying these techniques, it is possible to obtain about 0.5dB or more improvement over the union bound in AWGN channel and 1dB or more improvement in fading channels.