Bit error probability of distributed Turbo coded relay systems over quasi-static Rayleigh fading channels

As is known, distributed Turbo coding （DTC） performs close to the theoretic outage probability bound of a relay channel when correct decoding is assumed at the relay. However, decoding error is inevitable in practical fading channels due to the error-prone feature of radio channels, and the decoding error propagation in DTC scheme will severely degrade the error performance of the relay system. As a result, it is necessary to evaluate the error performance of the DTC scheme in multi-hop relaying wireless systems in practical fading channels. Moreover, the theoretical method of analysis provides an effective tool for obtaining the error performance besides lengthy simulations. In this article, the concept of equivalent signal-to-noise ratio （SNR） of the two-hop relay channel and the method of computing equivalent SNR are developed, and then the upper bound on the bit error probability （BEP） of DTC relay systems is analyzed by use of Turbo code＇s distance spectrum, the concept of uniform interleaver, the limit-before-averaging technique, and the union bound method. Both theoretical analysis and numerical simulation are implemented for relay systems with DTC scheme over quasi-static Rayleigh fading channels. The results show that the upper bound approaches the simulation results in the medium to high SNR region.