Linear Degrees of Freedom of the $X$ -Channel With Delayed CSIT

We establish the degrees of freedom (DoF) of the two-user X-channel with delayed channel knowledge at transmitters [i.e., delayed channel state information at the transmitters (CSIT)], assuming linear coding strategies at the transmitters. We derive a new upper bound and characterize the linear DoF of this network to be 6/5. The converse builds upon our development of a general lemma that shows that, if two distributed transmitters employ linear strategies, the ratio of the dimensions of received linear subspaces at the two receivers cannot exceed 3/2, due to delayed CSIT. As a byproduct, we also apply this general lemma to the three-user interference channel with delayed CSIT, thereby deriving a new upper bound of 9/7 on its linear DoF. This is the first bound that captures the impact of delayed CSIT on the DoF of this network, under the assumption of linear encoding strategies.

[1]  Abbas El Gamal,et al.  The feedback capacity of degraded broadcast channels (Corresp.) , 1978, IEEE Trans. Inf. Theory.

[2]  László Lovász,et al.  Submodular functions and convexity , 1982, ISMP.

[3]  Tie Liu,et al.  An Extremal Inequality Motivated by Multiterminal Information-Theoretic Problems , 2006, IEEE Transactions on Information Theory.

[4]  Syed A. Jafar,et al.  Interference Alignment and the Degrees of Freedom for the 3 User Interference Channel , 2007 .

[5]  Amir K. Khandani,et al.  Communication Over MIMO X Channels: Interference Alignment, Decomposition, and Performance Analysis , 2008, IEEE Transactions on Information Theory.

[6]  Shlomo Shamai,et al.  Degrees of Freedom Region of the MIMO $X$ Channel , 2008, IEEE Transactions on Information Theory.

[7]  Syed Ali Jafar,et al.  Degrees of freedom of wireless X networks , 2008, 2008 IEEE International Symposium on Information Theory.

[8]  Syed Ali Jafar,et al.  Interference Alignment and Degrees of Freedom of the $K$-User Interference Channel , 2008, IEEE Transactions on Information Theory.

[9]  Leandros Tassiulas,et al.  Broadcast erasure channel with feedback - Capacity and algorithms , 2009, 2009 Workshop on Network Coding, Theory, and Applications.

[10]  Mahesh K. Varanasi,et al.  The degrees of freedom region of the two-user MIMO broadcast channel with delayed CSIT , 2010, 2011 IEEE International Symposium on Information Theory Proceedings.

[11]  Amir K. Khandani,et al.  On the degrees of freedom of X channel with delayed CSIT , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[12]  David Gesbert,et al.  Degrees of Freedom of Time Correlated MISO Broadcast Channel With Delayed CSIT , 2012, IEEE Transactions on Information Theory.

[13]  Amir K. Khandani,et al.  On the degrees of freedom of MIMO X channel with delayed CSIT , 2011, 2012 IEEE International Symposium on Information Theory Proceedings.

[14]  Shlomo Shamai,et al.  Retrospective Interference Alignment Over Interference Networks , 2012, IEEE Journal of Selected Topics in Signal Processing.

[15]  Mohammad Ali Maddah-Ali,et al.  Completely Stale Transmitter Channel State Information is Still Very Useful , 2010, IEEE Transactions on Information Theory.

[16]  Mahesh K. Varanasi,et al.  The Degrees of Freedom Region and Interference Alignment for the MIMO Interference Channel With Delayed CSIT , 2011, IEEE Transactions on Information Theory.

[17]  Approximate capacity of the two-user MISO Broadcast Channel with delayed CSIT , 2013, 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[18]  David Tse,et al.  Interference alignment for the MIMO interference channel , 2013, ArXiv.

[19]  Amir Salman Avestimehr,et al.  A rank ratio inequality and the linear degrees of freedom of X-channel with delayed CSIT , 2013, 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[20]  Amir K. Khandani,et al.  On the Degrees of Freedom of K-User SISO Interference and X Channels With Delayed CSIT , 2011, IEEE Transactions on Information Theory.

[21]  Amir Salman Avestimehr,et al.  On degrees of freedom scaling in layered interference networks with delayed CSI , 2013, 2013 IEEE International Symposium on Information Theory.

[22]  Amir Salman Avestimehr,et al.  Layered Interference Networks With Delayed CSI: DoF Scaling With Distributed Transmitters , 2014, IEEE Transactions on Information Theory.

[23]  David Tse,et al.  Feasibility of Interference Alignment for the MIMO Interference Channel , 2013, IEEE Transactions on Information Theory.

[24]  Mohammad Ali Maddah-Ali,et al.  Communication through collisions: Opportunistic utilization of past receptions , 2013, IEEE INFOCOM 2014 - IEEE Conference on Computer Communications.

[25]  Amir Salman Avestimehr,et al.  Capacity Results for Binary Fading Interference Channels With Delayed CSIT , 2013, IEEE Transactions on Information Theory.

[26]  Ilan Shomorony,et al.  Degrees of Freedom of Two-Hop Wireless Networks: Everyone Gets the Entire Cake , 2012, IEEE Transactions on Information Theory.