Dirty Paper Arbitrarily Varying Channel with a State-Aware Adversary

In this paper, we take an arbitrarily varying channel (AVC) approach to examine the problem of writing on a dirty paper in the presence of an adversary. We consider an additive white Gaussian noise (AWGN) channel with an additive white Gaussian state, where the state is known non-causally to the encoder and the adversary, but not the decoder. We determine the randomized coding capacity of this AVC under the maximal probability of error criterion. Interestingly, it is shown that the jamming adversary disregards the state knowledge to choose a white Gaussian channel input which is independent of the state

On AVCs with Quadratic Constraints

In this work we study an Arbitrarily Varying Channel (AVC) with quadratic power constraints on the transmitter and a so-called "oblivious" jammer (along with additional AWGN) under a maximum probability of error criterion, and no private randomness between the transmitter and the receiver. This is in contrast to similar AVC models under the average probability of error criterion considered in [1], and models wherein common randomness is allowed [2] -- these distinctions are important in some communication scenarios outlined below. We consider the regime where the jammer's power constraint is smaller than the transmitter's power constraint (in the other regime it is known no positive rate is possible). For this regime we show the existence of stochastic codes (with no common randomness between the transmitter and receiver) that enables reliable communication at the same rate as when the jammer is replaced with AWGN with the same power constraint. This matches known information-theoretic outer bounds. In addition to being a stronger result than that in [1] (enabling recovery of the results therein), our proof techniques are also somewhat more direct, and hence may be of independent interest.Comment: A shorter version of this work will be send to ISIT13, Istanbul. 8 pages, 3 figure

Lattice Erasure Codes of Low Rank with Noise Margins

We consider the following generalization of an $(n,k)$ MDS code for application to an erasure channel with additive noise. Like an MDS code, our code is required to be decodable from any $k$ received symbols, in the absence of noise. In addition, we require that the noise margin for every allowable erasure pattern be as large as possible and that the code satisfy a power constraint. In this paper we derive performance bounds and present a few designs for low rank lattice codes for an additive noise channel with erasures

Universal decoders for channels with memory

Caption title.Includes bibliographical references (p. 14-15).Meir Feder and Amos Lapidoth

Near-Optimal Algorithms for Differentially-Private Principal Components

Principal components analysis (PCA) is a standard tool for identifying good low-dimensional approximations to data in high dimension. Many data sets of interest contain private or sensitive information about individuals. Algorithms which operate on such data should be sensitive to the privacy risks in publishing their outputs. Differential privacy is a framework for developing tradeoffs between privacy and the utility of these outputs. In this paper we investigate the theory and empirical performance of differentially private approximations to PCA and propose a new method which explicitly optimizes the utility of the output. We show that the sample complexity of the proposed method differs from the existing procedure in the scaling with the data dimension, and that our method is nearly optimal in terms of this scaling. We furthermore illustrate our results, showing that on real data there is a large performance gap between the existing method and our method.Comment: 37 pages, 8 figures; final version to appear in the Journal of Machine Learning Research, preliminary version was at NIPS 201