A new adaptive filter is proposed for the turbo decoding on Rayleigh fading channels with noisy channel estimates. In this book, by using the soft extrinsic information after each iteration of decoding, we re-estimate the channel and the minimum mean square error (m.m.s.e.) and further update the channel reliability factor and decision variables at each iteration. Simulations show that signal to noise (SNR) gain is improved by up to about 1dB at bit error probability of 3.5X10 DEGREES4. Based on this research, it would be more interesting for further researchers to develop an adaptive filter...