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We investigate the problem of guessing a discrete random variable Y under a privacy constraint dictated by another correlated discrete random variable X, where both guessing efficiency and privacy are assessed in terms of the probability of correct guessing. We define h(PXY,ε) as the maximum probability of correctly guessing Y given an auxiliary random variable Z, where the maximization is taken over...
We investigate the problem of the predictability of random variable Y under a privacy constraint dictated by random variable X, correlated with Y , where both predictability and privacy are assessed in terms of the minimum mean-squared error (MMSE). Given that X and Y are connected via a binary-input symmetric-output (BISO) channel, we derive the optimal random mapping PZ|Y such that the MMSE of Y...
Given a private source of information, Xn and a public correlated source, Yn, we study the problem of encoding the two-dimensional source (Xn; Yn) into an index J such that a remote party, knowing J and some external side information Zn, can losslessly recover Yn while any eavesdropper knowing J and possibly a correlated side information En can retrieve very little information about Xn. We give general...
The rate-privacy function is defined in [1] as a tradeoff between privacy and utility in a distributed private data system in which both privacy and utility are measured using mutual information. Here, we use maximal correlation in lieu of mutual information in the privacy constraint. We first obtain some general properties and bounds for maximal correlation and then modify the rate-privacy function...
We investigate the tradeoff between privacy and utility in a situation where both privacy and utility are measured in terms of mutual information. For the binary case, we fully characterize this tradeoff in case of perfect privacy and also give an upper-bound for the case where some privacy leakage is allowed. We then introduce a new quantity which quantifies the amount of private information contained...
The lossy source coding problem with feed-forward link was recently introduced in [1] and the corresponding rate-distortion function was derived in [2] and [3] for stationary and ergodic sources and for arbitrary sources with memory, respectively. The achievability schemes of [2] and [3] are mainly based on codetrees. In this work, we give an alternative proof of achievability for binary asymmetric...
The transmission of a single bit over the Poisson channel is considered when a noiseless feedback is available. We consider two cases: with and without peak power constraint. In the absence of peak power constraint, we show that sending one single bit reliably through a continuous-time Poisson channel requires at least half the energy of a photon. On the other hand, when a peak power constraint is...
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