Performance Bounds for Turbo Coded Half Duplex Relay Systems

We develop performance bounds for half duplex relay systems operating in decode-forward mode over additive white Gaussian noise (AWGN) channels. We consider the distributed turbo coding scheme [1] where the relay decodes the information obtained from the source, interleaves, re-encodes and forwards it to the destination. Unlike most other half duplex schemes proposed in the literature where the source remains silent during the relay transmission, the source and the relay in our scheme are allowed to transmit simultaneously in the same frequency band, in order to improve the overall spectral efficiency of the system. We employ the union bound on the average error probability for the general case of imperfect source to relay link assuming uniform interleaving at the source and the relay. We compare the bound with the simulation results obtained by the iterative decoding algorithm of [1] and show that for relatively large signal to noise ratios and large interleaver sizes the performance of the iterative algorithm is close to that predicted by the bound. The bounds are not restricted to turbo codes alone, i.e, they can be applied to other linear block codes including LDPC codes as well.