Abstract-This paper studies the relaying strategies and the approximate capacity of the classic three-node Gaussian relay channel, but where the noises at the relay and at the destination are correlated. It is shown that the capacity of such a relay channel can be achieved to within a constant gap of 1 2 log 2 3 = 0.7925 bits using a modified version of the noisy network coding strategy, where the quantization level at the relay is set in a correlation dependent way. As a corollary, this letter establishes that the conventional compress-and-forward scheme also achieves to within a constant gap to the capacity. In contrast, the decode-and-forward and the single-tap amplify-and-forward relaying strategies can have an infinite gap to capacity in the regime where the noises at the relay and at the destination are highly correlated, and the gain of the relay-to-destination link goes to infinity.
For the SISO Gaussian relay channel with noise correlation, REF shows that compress-and-forward achieves the capacity to within a constant additive gap.
Capacity of the Gaussian Relay Channel with Correlated Noises to Within a Constant Gap
IEEE Communications Letters
IEEE Communications Letters
Mathematics Computer Science