Oblivious lattice codes for Gaussian relay channels

Consider a slowly fading Gaussian relay channel where the source is not aware of channel state information (CSI) and the relay is only partially aware of CSI. As a single cooperation strategy, Decode-and-Forward (DF) or Compress-and-Forward (CF), is not the best for all channel states, the relay should be able to switch between them according to its CSI. However as the source cannot be aware of chosen cooperative strategy, it should use so called oblivious codes that perform equally well under different cooperative strategies. In this paper, we prove that doubly nested lattice codes is an oblivious code which can be used to achieve DF, CF or point-to-point rate in the relay channels. Using the oblivious lattice coding, the relay, according to its CSI, decides to use DF, CF or no cooperation at all. We show that inner bound on outage probability is significantly improved if the oblivious lattice code is used with selective coding strategy at the relay.