In this paper we propose a method that aims at reducing the complexity of convolutional and turbo decoding. Some calculations performed in decoding processing can be eliminated based on reliability thresholds. For convolutional and turbo decoding, the complexity is proportional to the number of branches in the trellis. For convolutional decoding, based on the Viterbi algorithm, we define reliability thresholds for the received samples of the signal and show that is possible to eliminate some branches in the trellis and consequently to reduce the complexity. For turbo decoding based on MAP algorithm, we set a threshold to classify each information bit log likelihood ratio (LLR). When the LLR is reliable, we take a decision on information bits and eliminate some branches in the trellis. Furthermore, we also define a criterion for stopping decoding wich further reduces the complexity. In this paper we show that it is possible to reduce decoding complexity of convolutional codes almost 80 % without performance degradation when compared to Viterbi algorithm over Rayleigh fading channels. In turbo decoding, we show that complexity varies with (Formula presented.) and it is reduced when more iterations are computed, tending to zero for higher iterations.