Information Dimension and the Degrees of Freedom of the Interference Channel

The degrees of freedom (DoFs) of the K -user Gaussian interference channel determine the asymptotic growth of the maximal sum rate as a function of the signal-to-noise ratio. Subject to a very general sufficient condition on the cross-channel gains, we give a formula for the DoFs of the scalar interference channel as a function of the deterministic channel matrix, which involves maximization of a sum of information dimensions over K scalar input distributions. Known special cases are recovered, and even generalized in certain cases with unified proofs.