Related papers: How to send a real number using a single bit (and …
When digital data are transmitted over a noisy channel, it is important to have a mechanism allowing recovery against a limited number of errors. Normally, a user string of 0's and 1's, called bits, is encoded by adding a number of…
What is the value of a single bit to a guesser? We study this problem in a setup where Alice wishes to guess an i.i.d. random vector, and can procure one bit of information from Bob, who observes this vector through a memoryless channel. We…
A distributed adaptive algorithm to estimate a time-varying signal, measured by a wireless sensor network, is designed and analyzed. One of the major features of the algorithm is that no central coordination among the nodes needs to be…
In realistic distributed optimization scenarios, individual nodes possess only partial information and communicate over bandwidth constrained channels. For this reason, the development of efficient distributed algorithms is essential. In…
We study common randomness where two parties have access to i.i.d. samples from a known random source, and wish to generate a shared random key using limited (or no) communication with the largest possible probability of agreement. This…
Suppose we have a memory storing $0$s and $1$s and we want to estimate the frequency of $1$s by sampling. We want to do this I/O-efficiently, exploiting that each read gives a block of $B$ bits at unit cost; not just one bit. If the input…
We study first-order optimization algorithms under the constraint that the descent direction is quantized using a pre-specified budget of $R$-bits per dimension, where $R \in (0 ,\infty)$. We propose computationally efficient optimization…
We consider the problem of solving a distributed optimization problem using a distributed computing platform, where the communication in the network is limited: each node can only communicate with its neighbours and the channel has a…
An energy-limited source trying to transmit multiple packets to a destination with possibly different sizes is considered. With limited energy, the source cannot potentially transmit all bits of all packets. In addition, there is a delay…
Given a budget and arbitrary cost for selecting each node, the budgeted influence maximization (BIM) problem concerns selecting a set of seed nodes to disseminate some information that maximizes the total number of nodes influenced (termed…
We consider the one-bit quantizer that minimizes the mean squared error for a source living in a real Hilbert space. The optimal quantizer is a projection followed by a thresholding operation, and we provide methods for identifying the…
We consider the problem of mapping a logical quantum circuit onto a given hardware with limited two-qubit connectivity. We model this problem as an integer linear program, using a network flow formulation with binary variables that includes…
Distributed graph signal processing algorithms require the network nodes to communicate by exchanging messages in order to achieve a common objective. These messages have a finite precision in realistic networks, which may necessitate to…
A central server needs to perform statistical inference based on samples that are distributed over multiple users who can each send a message of limited length to the center. We study problems of distribution learning and identity testing…
We show that any classical two-way communication protocol with shared randomness that can approximately simulate the result of applying an arbitrary measurement (held by one party) to a quantum state of $n$ qubits (held by another), up to…
Rejection sampling is a popular method used to generate numbers that follow some given distribution. We study the use of this method to generate random numbers in the unit interval from increasing probability density functions. We focus on…
Large data sets often require performing distributed statistical estimation, with a full data set split across multiple machines and limited communication between machines. To study such scenarios, we define and study some refinements of…
We develop the resource theory of private randomness extraction in the distributed and device-dependent scenario. We begin by introducing the notion of independent random bits, which are bipartite states containing ideal private randomness…
We study the mean estimation problem under communication and local differential privacy constraints. While previous work has proposed \emph{order}-optimal algorithms for the same problem (i.e., asymptotically optimal as we spend more bits),…
Alice and Bob want to run a protocol over a noisy channel, where a certain number of bits are flipped adversarially. Several results take a protocol requiring $L$ bits of noise-free communication and make it robust over such a channel. In a…