Related papers: How Hard is Computing Parity with Noisy Communicat…
We consider the problem of computing a perfect matching problem in a synchronous distributed network, where the network topology corresponds to a complete bipartite graph. The communication between nodes is restricted to activating…
The radio network model is a well-studied model of wireless, multi-hop networks. However, radio networks make the strong assumption that messages are delivered deterministically. The recently introduced noisy radio network model relaxes…
The rate regions of many variations of the standard and wire-tap channels have been thoroughly explored. Secrecy capacity characterizes the loss of rate required to ensure that the adversary gains no information about the transmissions.…
We consider the problem of minimizing the number of broadcasts for collecting all sensor measurements at a sink node in a noisy broadcast sensor network. Focusing first on arbitrary network topologies, we provide (i) fundamental limits on…
We describe a slightly sub-exponential time algorithm for learning parity functions in the presence of random classification noise. This results in a polynomial-time algorithm for the case of parity functions that depend on only the first…
The process of state preparation, its transmission and subsequent measurement can be classically simulated through the communication of some amount of classical information. Recently, we proved that the minimal communication cost is the…
Alice and Bob want to know if two strings of length n are almost equal. That is, do they differ on \textit{at most} a bits? Let 0\leq a\leq n-1. We show that any deterministic protocol, as well as any error-free quantum protocol (C*…
In this paper we study the two player randomized communication complexity of the sparse set disjointness and the exists-equal problems and give matching lower and upper bounds (up to constant factors) for any number of rounds for both of…
As techniques for fault-tolerant quantum computation keep improving, it is natural to ask: what is the fundamental lower bound on redundancy? In this paper, we obtain a lower bound on the redundancy required for $\epsilon$-accurate…
We present an upper bound on the error probability achievable using variable-length stop feedback codes, for a fixed size of the information payload and a given constraint on the maximum latency and the average service time. Differently…
We establish the capacity of a class of communication channels introduced in [1]. The $n$-letter input from a finite alphabet is passed through a discrete memoryless channel $P_{Z|X}$ and then the output $n$-letter sequence is uniformly…
We fully determine the communication complexity of approximating matrix rank, over any finite field $\mathbb{F}$. We study the most general version of this problem, where $0\leq r<R\leq n$ are given integers, Alice and Bob's inputs are…
Consensus and Broadcast are two fundamental problems in distributed computing, whose solutions have several applications. Intuitively, Consensus should be no harder than Broadcast, and this can be rigorously established in several models.…
We consider the situation in which a transmitter attempts to communicate reliably over a discrete memoryless channel while simultaneously ensuring covertness (low probability of detection) with respect to a warden, who observes the signals…
We use a combination of analytical and numerical techniques to calculate the noise threshold and resource requirements for a linear optical quantum computing scheme based on parity-state encoding. Parity-state encoding is used at the lowest…
Motivated by the application of point-to-point communication networks and biological storage, we investigate new achievability bounds for noisy permutation channels with strictly positive and full-rank square matrices. Our new bounds use…
We prove new bounds on the quantum communication complexity of the disjointness and equality problems. For the case of exact and non-deterministic protocols we show that these complexities are all equal to n+1, the previous best lower bound…
This paper studies the problem of finding the exact ranking from noisy comparisons. A comparison over a set of $m$ items produces a noisy outcome about the most preferred item, and reveals some information about the ranking. By repeatedly…
We obtain strict upper bounds on the bit transmission rate for communication of Classical bit codewords over Quantum channels. Albeit previous arguments in arXiv: 1804.01797 which have demonstrated that lower bounds can be shown to hold for…
Sorting is a fundamental problem in computer science. In the classical setting, it is well-known that $(1\pm o(1)) n\log_2 n$ comparisons are both necessary and sufficient to sort a list of $n$ elements. In this paper, we study the Noisy…