Opportunistic noisy network coding for fading parallel relay networks

The recently developed noisy network coding naturally extends compress-forward coding for the relay channel by Cover and El Gamal to arbitrary relay networks. In particular, the noisy network coding scheme achieves the best known capacity lower bound for general Gaussian networks. Motivated by the recent development of noisy network coding, we propose a novel extension of noisy network coding specialized for the fading parallel relay network. In the new scheme, the relay observation is opportunistically compressed by adapting on the local channel state information of the source-relay link. More specifically, each relay node opportunistically compresses the collection of output symbols with channel gains above a certain threshold, and forwards the digital compression to the destination node using independent Gaussian codes. To present the potential of the new scheme, we focus on the symmetric setting in which the channel coefficients within each hop are identically and independently distributed. We show that in the large number of relays regime, our scheme achieves the capacity while outperforming other schemes such as amplify-forward and decode-forward. Our result demonstrates that adaptation using channel state information at the receiver side can be beneficial.