In this study, we consider the selective combining in hybrid cooperative networks (SCHCNs scheme) with one source node, one destination node and @math relay nodes. In the SCHCN scheme, each relay first adaptively chooses between amplify-and-forward protocol and decode-and-forward protocol on a per frame basis by examining the error-detecting code result, and @math ( @math ) relays will be selected to forward their received signals to the destination. We first develop a signal-to-noise ratio (SNR) threshold-based frame error rate (FER) approximation model. Then, the theoretical FER expressions for the SCHCN scheme are derived by utilizing the proposed SNR threshold-based FER approximation model. The analytical FER expressions are validated through simulation results.
It is known that the frame error rate of turbo codes on quasi-static fading channels can be accurately approximated using the convergence threshold of the corresponding iterative decoder. This paper considers quasi-static fading channels and demonstrates that non-iterative schemes can also be characterized by a similar threshold based on which their frame error rate can be readily estimated. In particular, we show that this threshold is a function of the probability of successful frame detection in additive white Gaussian noise, normalized by the squared instantaneous signal-to-noise ratio. We apply our approach to uncoded binary phase shift keying, convolutional coding and turbo coding and demonstrate that the approximated frame error rate is within 0.4 dB of the simulation results. Finally, we introduce performance evaluation plots to explore the impact of the frame size on the performance of the schemes under investigation. Proper selection of a signal-to-noise ratio threshold largely determines the tightness of an approximation to the frame error rate of a system over a quasistatic fading channel. It is demonstrated that the expression for the optimal threshold value, which has been established for single-input single-output (SISO) channels, remains unchanged for the general case of multiple-input multiple-output (MIMO) channels. We introduce a simple technique for analyzing the iterative decoder that is broadly applicable to different classes of codes defined over graphs in certain fading as well as additive white Gaussian noise (AWGN) channels. The technique is based on the observation that the extrinsic information from constituent maximum a posteriori (MAP) decoders is well approximated by Gaussian random variables when the inputs to the decoders are Gaussian. The independent Gaussian model implies the existence of an iterative decoder threshold that statistically characterizes the convergence of the iterative decoder. Specifically, the iterative decoder converges to zero probability of error as the number of iterations increases if and only if the channel E sub b N sub 0 exceeds the threshold. Despite the idealization of the model and the simplicity of the analysis technique, the predicted threshold values are in excellent agreement with the waterfall regions observed experimentally in the literature when the codeword lengths are large. Examples are given for parallel concatenated convolutional codes, serially concatenated convolutional codes, and the generalized low-density parity-check (LDPC) codes of Gallager and Cheng-McEliece (1996). Convergence-based design of asymmetric parallel concatenated convolutional codes (PCCC) is also discussed.