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

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3 Author(s)
Lashgari, S. ; Sch. of Electr. & Comput. Eng., Cornell Univ., Ithaca, NY, USA ; Avestimehr, A.S. ; Suh, C.

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.

Published in:

Information Theory, IEEE Transactions on  (Volume:60 ,  Issue: 4 )

Date of Publication:

April 2014

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