Information Dimension and the Degrees of Freedom of the Interference Channel

• Published in: IEEE transactions on information theory Vol. 61; no. 1; pp. 256 - 279
• Main Authors: Wu, Yihong, Shamai Shitz, Shlomo, Verdu, Sergio
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic methods; degrees of freedom; Entropy; high-SNR channels; information dimension; Information theory; Integrated circuits; interference channel; Interference channels; Matrix; Multiuser information theory; Mutual information; Random variables; Shannon theory; Signal to noise ratio; sumset entropy inequalities; Zinc; information dimension; interference channel; degrees of freedom; high-SNR channels; Shannon theory; Multiuser information theory; sumset entropy inequalities
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2014.2366238

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.