The number of quantization bits of the input signals $X_k$,$Y_k$ need to be optimally determined through the trade-off between the H/W complexity and the BER performance in Turbo codes applications. Also, an effective means to incorporate a channel reliability $L_c$ in the Log-MAP-based Turbo decoding is highly required. because it has a major effect on both the complexity and the performance. In this paper, a novel bit-shifting approach that substitutes for the multiplying is proposed so as to effectively incorporate. $L_c$ in Turbo decoding. The optimal number of quantization bits of $X_k$,$Y_k$ is investigated through Monte-Carlo simulations assuming that bit-shifting approach is adopted. In addition. The effects of an incorrect estimation of noise variance on the performance of Turbo codes is investigated. There is a confined range in which the effects of an incorrect estimation can be ignored.