Aligned Image Sets under Channel Uncertainty: Settling a Conjecture by Lapidoth, Shamai and Wigger on the Collapse of Degrees of Freedom under Finite Precision CSIT.

摘要: A conjecture made by Lapidoth, Shamai and Wigger at Allerton 2005 (also an open problem presented ITA 2006) states that the DoF of a 2 user broadcast channel, where transmitter is equipped with antennas each 1 antenna, must collapse under finite precision CSIT. In this work we prove true in all non-degenerate settings (e.g., probability density function unknown channel coefficients exists bounded). The even when perfect knowledge for one available to transmitter. This also settles related recent Tandon et al. key our proof bound on number codewords can cast same image (within noise distortion) undesired receiver whose subject CSIT, while remaining resolvable desired precisely known We are able generalize result along two directions. First, if peak allowed scale as O(P^(\alpha/2)), representing concentration (improving CSIT) due to, e.g., quantized feedback rate (\alpha/2)\log(P), then bounded above 1+\alpha, which achievable feedback. Second, K single antenna receiver. Here uncertainty. directly implies unity uncertainty general K-user interference MxN X networks well.