This paper analyzes the performance of relay networks with channel coding in low and medium Signal-to-Noise Ratio (SNR) regime. In particular, we study the three-node relay network in the quasi-static block Rayleigh fading channel plus additive white Gaussian noise. Estimate-and-forward (EF) relay protocol is used. In order to achieve high spectrum efficiency, the relay can either forward the whole or a part of the estimated codeword to the destination. The contributions of the paper are as follows: i) First, we compute an upper bound of the Bit Error Rate (BER) of the proposed scheme. ii) Second, from the upper bound, we derive a so-called instantaneous diversity order in low and medium SNR region which is essential to practical systems. The instantaneous diversity depends on both the amount of information forwarded by the relay and the minimum distance of the channel code. Interestingly, the proposed scheme can achieve full diversity gain in a given SNR region of interest (such as BER ≤ 10-5) while obtaining 32% spectrum efficiency improvement compared to classical relay network under appropriate conditions. The analysis is checked by simulation.