Compress-forward Relaying over Parallel Gaussian Channels

We propose a compress-forward (CF) strategy for relaying over parallel Gaussian channels. The proposed CF strategy compresses received signals at the relay under a constraint on the product of their allowable distortions and forwards them to the destination over all subchannels. Power allocation over all subchannels at both the source and the relay and bit allocation for compressing received signals at the relay are jointly optimized under a total power constraint on each node. The proposed CF strategy is shown to generalize a previous CF strategy in which the relay compresses the received signal from the i-th incoming subchannel and forwards it only through the i-th outgoing subchannel. We show that, if the incoming and outgoing subchannels at the relay are suitably matched, both CF strategies have similar performance. Otherwise, the gap between their performances becomes significant.