Related papers: How Hard is Computing Parity with Noisy Communicat…
A common scenario in distributed computing involves a client who asks a server to perform a computation on a remote computer. An important problem is to determine the minimum amount of communication needed to specify the desired…
We present a two-step decoder for the parity code and evaluate its performance in code-capacity and faulty-measurement settings. For noiseless measurements, we find that the decoding problem can be reduced to a series of repetition codes…
We consider the model of communication where wireless devices can either switch their radios off to save energy, or switch their radios on and engage in communication. We distill a clean theoretical formulation of this problem of minimizing…
Fault-tolerant consensus is about reaching agreement on some of the input values in a limited time by non-faulty autonomous processes, despite of failures of processes or communication medium. This problem is particularly challenging and…
Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error…
An $n$-bit string is encoded as a sequence of non-orthogonal quantum states. The parity bit of that $n$-bit string is described by one of two density matrices, $\rho_0^{(n)}$ and $\rho_1^{(n)}$, both in a Hilbert space of dimension $2^n$.…
We study noisy broadcast networks with local cache memories at the receivers, where the transmitter can pre-store information even before learning the receivers' requests. We mostly focus on packet-erasure broadcast networks with two…
We consider the problem of data exchange by a group of closely-located wireless nodes. In this problem each node holds a set of packets and needs to obtain all the packets held by other nodes. Each of the nodes can broadcast the packets in…
We derive bounds on the asymptotic density of parity-check matrices and the achievable rates of binary linear block codes transmitted over memoryless binary-input output-symmetric (MBIOS) channels. The lower bounds on the density of…
Energy is often the most constrained resource in networks of battery-powered devices, and as devices become smaller, they spend a larger fraction of their energy on communication (transceiver usage) not computation. As an imperfect proxy…
For nearly two decades, population protocols have been extensively studied, yielding efficient solutions for central problems in distributed computing, including leader election, and majority computation, a predicate type in Presburger…
We consider the N-relay Gaussian diamond network where a source node communicates to a destination node via N parallel relays through a cascade of a Gaussian broadcast (BC) and a multiple access (MAC) channel. Introduced in 2000 by Schein…
Broadcasting on trees is a fundamental model from statistical physics that plays an important role in information theory, noisy computation and phylogenetic reconstruction within computational biology and linguistics. While this model…
This paper studies the classification of high-dimensional Gaussian signals from low-dimensional noisy, linear measurements. In particular, it provides upper bounds (sufficient conditions) on the number of measurements required to drive the…
We introduce and study the communication complexity of computing the inner product of two vectors, where the input is restricted w.r.t. a norm $N$ on the space $\mathbb{R}^n$. Here, Alice and Bob hold two vectors $v,u$ such that $\|v\|_N\le…
We present a square root limit on the amount of information transmitted reliably and with low probability of detection (LPD) over additive white Gaussian noise (AWGN) channels. Specifically, if the transmitter has AWGN channels to an…
Population protocols are a model of distributed computing, in which $n$ agents with limited local state interact randomly, and cooperate to collectively compute global predicates. An extensive series of papers, across different communities,…
In analogy with its classical counterpart, a noisy quantum channel is characterized by a loss, a quantity that depends on the channel input and the quantum operation performed by the channel. The loss reflects the transmission quality: if…
We prove tight bounds of Theta(k log k) queries for non-adaptively testing whether a function f:{0,1}^n -> {0,1} is a k-parity or far from any k-parity. The lower bound combines a recent method of Blais, Brody and Matulef [BBM11] to get…
The estimation of parameters characterizing dynamical processes is central to science and technology. The estimation error changes with the number N of resources employed in the experiment (which could quantify, for instance, the number of…