Degrees of freedom in vector interference channels
AuthorsDavid Stotz and Helmut Bölcskei
ReferenceIEEE Transactions on Information Theory, Vol. 62, No. 7, pp. 4172-4197, July 2016
AbstractThis paper continues the Wu-Shamai-Verdú program  on characterizing the degrees of freedom (DoF) of interference channels (ICs) through Rényi information dimension. Specifically, we find a single-letter formula for the DoF of vector ICs, encompassing multiple-input multiple-output (MIMO) ICs, time- and/or frequency-selective ICs, and combinations thereof, as well as scalar ICs as considered in . The DoF-formula we obtain lower-bounds the DoF of all channels—with respect to the choice of the channel matrix—and upper-bounds the DoF of almost all channels. It applies to a large class of noise distributions, and its proof is based on an extension of a result by Guionnet and Shlyakthenko  to the vector case in combination with the Ruzsa triangle inequality for differential entropy introduced by Kontoyiannis and Madiman . As in scalar ICs, achieving full DoF requires the use of singular input distributions. Strikingly, in the vector case it suffices to enforce singularity on the joint distribution of each transmit vector. This can be realized through signaling in subspaces of the ambient signal space, which is in accordance with the idea of interference alignment, and, most importantly, allows the scalar entries of the transmit vectors to have non-singular distributions. The DoF-formula for vector ICs we obtain enables a unified treatment of “classical” interference alignment à la Cadambe and Jafar , and Maddah-Ali et al. , and the number-theoretic schemes proposed in , . Moreover, it allows to calculate the DoF achieved by new signaling schemes for vector ICs. We furthermore recover the result by Cadambe and Jafar on the non-separability of parallel ICs  and we show that almost all parallel ICs are separable in terms of DoF. Finally, our results apply to complex vector ICs, thereby extending the main findings of  to the complex case.
An Online Addendum to the paper is available here.
Download this document:
Copyright Notice: © 2016 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.