GDoF of the MISO BC: Bridging the gap between finite precision CSIT and perfect CSIT

This work bridges the gap between sharply contrasting results on the degrees of freedom of the K user broadcast channel where the transmitter is equipped with K transmit antennas and each of the K receivers is equipped with a single antenna. This channel has K DoF when channel state information at the transmitter (CSIT) is perfect, but as shown recently, it has only 1 DoF when the CSIT is limited to finite precision. By considering the full range of partial CSIT assumptions parameterized by β ⋯ [0,1], such that the strength of the channel estimation error terms scales as ∼ SNR-β relative to the channel strengths which scale as ∼ SNR, it is shown that this channel has 1 - β + Kβ DoF. For K = 2 users with arbitrary βij parameters, the DoF are shown to be 1 + mini,j βij. To explore diversity of channel strengths, the results are further extended to the symmetric Generalized Degrees of Freedom setting where the direct channel strengths scale as ∼ SNR and the cross channel strengths scale as ∼ SNRα, α ⋯ [0,1], β ⋯ [0,α]. Here, the roles of α and β are shown to counter each other on equal terms, so that the sum GDoF value in the K user setting is (α - β) + K(1 - (α-β )) and for the 2 user setting with arbitrary βij, is 2 - α + mini,j βij

Automatic Identification of AltLexes using Monolingual Parallel Corpora

The automatic identification of discourse relations is still a challenging task in natural language processing. Discourse connectives, such as "since" or "but", are the most informative cues to identify explicit relations; however discourse parsers typically use a closed inventory of such connectives. As a result, discourse relations signaled by markers outside these inventories (i.e. AltLexes) are not detected as effectively. In this paper, we propose a novel method to leverage parallel corpora in text simplification and lexical resources to automatically identify alternative lexicalizations that signal discourse relation. When applied to the Simple Wikipedia and Newsela corpora along with WordNet and the PPDB, the method allowed the automatic discovery of 91 AltLexes.Comment: 6 pages, Proceedings of Recent Advances in Natural Language Processing (RANLP 2017

Sum-set inequalities from aligned image sets: Instruments for robust GDoF bounds

We present sum-set inequalities specialized to the generalized degrees of freedom (GDoF) framework. These are information theoretic lower bounds on the entropy of bounded density linear combinations of discrete, power-limited dependent random variables in terms of the joint entropies of arbitrary linear combinations of new random variables that are obtained by power level partitioning of the original random variables. The bounds are useful instruments to obtain GDoF characterizations for wireless interference networks, especially with multiple antenna nodes, subject to arbitrary channel strength and channel uncertainty levels