An Efficient Coding Scheme for the AWGN Relay Network with Receiver-Transmitter Feedback

In this article, the relay network (RN) with receiver-transmitter feedback is investigated. First, we propose an efficient feedback coding scheme for the additive white Gaussian noise (AWGN) RN with noiseless receiver-transmitter feedback, which generalizes the Schalkwijk-Kailath (SK) type scheme for the AWGN channel with a single relay and noiseless receiver-transmitter feedback. The corresponding achievable rate of our proposed scheme is obtained under fixed coding block length and the receiver's decoding error probability, and it is shown that channel feedback significantly enhances the achievable rate of the same model without feedback. Then, we extend the above scheme to the same model with an AWGN feedback channel, where a modulo lattice function is applied to mitigate the impact of the feedback channel noise on the performance of the SK-type scheme. Finally, we further extend our proposed scheme to the quasi-static Rayleigh fading RN by using a precoding strategy. The results of this article are further explained via numerical examples, and this article provides a new method to construct low complexity coding schemes for relay networks.