A.3 Review of Information-Theoretic Notions 287 The Shannon capacity of an additive white Gaussian channel Y = X + Z with E|X| 2 P and Z CN(0, N) is given by: P . N C = log 2 1 + (A.17) In the case of multi-dimensional channel inputs and outputs, y = Hx + z, the Shannon capacity becomes: 1 HQH H N C = max log 2 I r + Q (A.18) where r is the dimension of the channel output, Q = E(xx H ), Tr(Q) P, and |M| = Det(M).