Adriano Pastore

Locally differentially-private distribution estimation

We consider a setup in which confidential i.i.d. samples X1, ..., Xn from an unknown discrete distribution PX are passed through a discrete memoryless privatization channel (a.k.a. mechanism) which guarantees an ϵ-level of local differential privacy. For a given ϵ, the channel should be designed such that an estimate of the source distribution based on the channel outputs converges as fast as possible to the exact value PX. For this purpose we consider two metrics of estimation accuracy: the expected mean-square error and the expected Kullback-Leibler divergence. We derive their respective normalized first-order terms (as n → ∞), which for a given target privacy ϵ represent the factor by which the sample size must be augmented so as to achieve the same estimation accuracy as that of an identity (non-privatizing) channel. We formulate the privacy-utility tradeoff problem as being that of minimizing said first-order term under a privacy constraint ϵ. A converse bound is stated which bounds the optimal tradeoff away from the origin. Inspired by recent work on the optimality of staircase mechanisms (albeit for objectives different from ours), we derive an achievable tradeoff based on circulant step mechanisms. Within this finite class, we determine the optimal step pattern.

A Rate-Splitting Approach to Fading Channels With Imperfect Channel-State Information

As shown by Médard, the capacity of fading channels with imperfect channel-state information can be lower-bounded by assuming a Gaussian channel input X with power P and by upper-bounding the conditional entropy h(X|Y, Ĥ) by the entropy of a Gaussian random variable with variance equal to the linear minimum mean-square error in estimating X from (Y, Ĥ). We demonstrate that, using a rate-splitting approach, this lower bound can be sharpened: by expressing the Gaussian input X as the sum of two independent Gaussian variables X1 and X2 and by applying Médards lower bound first to bound the mutual information between X1 and Y while treating X2 as noise, and by applying it a second time to the mutual information between X2 and Y while assuming X1 to be known, we obtain a capacity lower bound that is strictly larger than Médards lower bound. We then generalize this approach to an arbitrary number L of layers, where X is expressed as the sum of L independent Gaussian random variables of respective variances Pℓ, ℓ = 1, ... , L summing up to P. Among all such rate-splitting bounds, we determine the supremum over power allocations Pℓ and total number of layers L. This supremum is achieved for L →∞ and gives rise to an analytically expressible capacity lower bound. For Gaussian fading, this novel bound is shown to converge to the Gaussian-input mutual information as the signal-to-noise ratio (SNR) grows, provided that the variance of the channel estimation error H - Ĥ tends to zero as the SNR tends to infinity.

Joint pilot and precoder design for optimal throughput

For single-user, multiple-input multiple-output (MIMO) channels with Rayleigh fading correlated at the transmitter side, and where the receiver only has partial channel knowledge in form of an MMSE channel estimate, we study the joint optimization of the linear precoder and the pilot (training) sequence under the constraint of prescribed transmit power and training energy budgets. Although this joint problem is generally not convex itself, we can show that the two marginal problems of optimizing either the pilot sequence or the precoder when the other variable is fixed, are convex. Furthermore, we characterize the jointly optimal transmit and training directions. Finally, we propose a full characterization of the Pareto efficient joint power loading strategies for the case of two transmit antennas, and illustrate the behavior of the jointly optimal solution.

Sharpened capacity lower bounds of fading MIMO channels with imperfect CSI

A well-established capacity lower bound of multiple-input multiple-output (MIMO) single-user fading channels operating with imperfect receiver-side channel-state information (CSI) is improved using a simple rate-splitting and successive-decoding scheme. The potential improvement is shown to increase with the number of allowed decoding steps (layers) to such extent that the best layering strategy is approached in the limit as the number of layers tends to infinity. We give a general analytic expression of this limit, which constitutes a new capacity lower bound that is sharper than the conventional bound. Using large random matrix theory, we derive an asymptotic approximation of this novel bound, which is shown via numerical simulation to be highly accurate over the whole range of signal-to-noise ratios.

Improved capacity lower bounds for fading channels with imperfect CSI using rate splitting

As shown by Medard (“The effect upon channel capacity in wireless communications of perfect and imperfect knowledge of the channel,” IEEE Trans. Inform. Theory, May 2000), the capacity of fading channels with imperfect channel-state information (CSI) can be lower-bounded by assuming a Gaussian channel input X, and by upper-bounding the conditional entropy h(X\Y, Ĥ), conditioned on the channel output Y and the CSI Ĥ, by the entropy of a Gaussian random variable with variance equal to the linear minimum mean-square error in estimating X from (Y, Ĥ). We demonstrate that, by using a rate-splitting approach, this lower bound can be sharpened: we show that by expressing the Gaussian input X as as the sum of two independent Gaussian variables X(1) and X(2), and by applying Medards lower bound first to analyze the mutual information between X(1) and Y conditioned on Ĥ while treating X(2) as noise, and by applying the lower bound then to analyze the mutual information between X(2) and Y conditioned on (X(1), Ĥ), we obtain a lower bound on the capacity that is larger than Medards lower bound.

On a rate region approximation of MIMO channels under partial CSI

When the receiver of a multiple-input multiple-output (MIMO) channel does not know the channel state, but only a linear estimate thereof, the rates achieved with (suboptimal) Gaussian codebooks become difficult to compute. However, one can resort to upper and lower bounds known from literature. Extending the ideas of earlier works on the resource allocation (time and energy) between pilot and data symbols, we first show that, at high SNR, the optimal training length is min(M,N) (where M and N are the number of receive and transmit antennas), and that in no case more than half the coherence time should be used for training. By simple arguments, we show that the basic training scheme—which allocates separate time slots for training and data transmission—achieves the diversity-multiplexing tradeoff of block-fading channels. In a second part, we propose a generalization of the mutual information bounds to inner and outer rate region bounds of the multiple-access channel.

On a Mutual Information and a Capacity Bound Gap of Pilot-Aided MIMO Channels

For single-user MIMO channels with partial receiver CSI, we study the difference between inner and outer bounds of the mutual information achieved with Gaussian codebooks, as well as a related difference between capacity inner and outer bounds. In contrast to previous studies, we assume that the channel estimation error statistics are not given a priori, but depend on the parameters of a training routine, in which a pilot sequence is transmitted, and where the channel realization is linearly estimated. Under these conditions, we successively determine analytic upper and lower bounds on the mutual information bound gap. We further study the asymptotic behavior of said bound gaps for high SNR and a large number of antennas. This allows us to prove, for example, that for MISO channels and a certain class of semicorrelated MIMO channels, when the training and transmit power levels are equal, the capacity is approached to within min(N_Tx,N_Rx) bits by the capacity bounds, where N_Tx and N_Rx stand for the number of transmit and receive antennas, respectively.

Coordinated Shared Spectrum Precoding With Distributed CSIT

In this paper, the operation of a licensed shared access system is investigated, considering downlink communication. The system comprises a multiple-input-single-output (MISO) incumbent transmitter (TX)-receiver (RX) pair, which offers a spectrum sharing opportunity to a MISO licensee TX-RX pair. Our main contribution is the design of a coordinated transmission scheme, inspired by the underlay cognitive radio (CR) approach, with the aim of maximizing the average rate of the licensee, subject to an average rate constraint for the incumbent. In contrast to most prior works on the underlay CR, the coordination of the two TXs takes place under a realistic channel state information (CSI) scenario, where each TX has solely access to the instantaneous direct channel of its served terminal. Such a CSI knowledge setting brings about a formulation based on the theory of Team Decisions, whereby the TXs aim at optimizing a common objective given the same constraint set, on the basis of individual channel information. Consequently, a novel set of applicable precoding schemes consisting in letting the two TXs cooperate on the basis of the statistical information is proposed. We verify by simulations that this novel, practically relevant, coordinated precoding scheme outperforms the standard underlay CR approach.

Rate balancing in the vector BC with erroneous CSI at the receivers

For the vector broadcast channel (BC), the case of erroneous channel state information (CSI) at the receiver is considered. Employing a well established lower bound for the mutual information with Gaussian signaling, a rate balancing problem is formulated where the rates of the different users are maximized under a transmit power constraint, but the rates of the different users have fixed ratios. A duality w.r.t. the signal-to-interference-and-noise ratio (SINR) between the vector BC with erroneous receiver CSI and an appropriately constructed vector multiple access channel (MAC) is established. Based on the observation that an interference function can be defined in the dual vector MAC that is standard, an iterative algorithm can be found for an appropriately formulated quality-of-service (QoS) optimization that is used for solving the balancing problem.

Towards an algebraic network information theory: Simultaneous joint typicality decoding

Recent work has employed joint typicality encoding and decoding of nested linear code ensembles to generalize the compute-forward strategy to discrete memoryless multiple-access channels (MACs). An appealing feature of these nested linear code ensembles is that the coding strategies and error probability bounds are conceptually similar to classical techniques for random i.i.d. code ensembles. In this paper, we consider the problem of recovering K linearly independent combinations over a K-user MAC, i.e., recovering the messages in their entirety via nested linear codes. While the MAC rate region is well-understood for random i.i.d. code ensembles, new techniques are needed to handle the statistical dependencies between competing codeword K-tuples that occur in nested linear code ensembles.