When Feedback Doubles the Prelog in AWGN Networks

We demonstrate that the sum-rate capacity of a memoryless Gaussian network at high signal-to-signal ratio (SNR) can be asymptotically doubled when feedback is available. To demonstrate this phenomenon we study two networks: the one-to-two scalar Gaussian broadcast channel (BC) and the twoto-two scalar Gaussian interference channel (IC). For the broadcast channel we show that if the noise sequences experienced by the two receivers are anticorrelated, then, at high SNR, feedback doubles the sum-rate capacity. However, this result no longer holds if the feedback is noisy. For the interference channel we show that if the cross gain is positive and if the noises experienced by the two receivers are anticorrelated and of the same variance, then feedback doubles the high SNR sum-rate capacity.