Related papers: Term Coding and Dispersion: A Perfect-vs-Rate Comp…
We introduce \emph{Term Coding}, a novel framework for analysing extremal problems in discrete mathematics by encoding them as finite systems of \emph{term equations} (and, optionally, \emph{non-equality constraints}). In its basic form,…
Term Coding asks: given a finite system of term identities $\Gamma$ in $v$ variables, how large can its solution set be on an $n$--element alphabet, when we are free to choose the interpretations of the function symbols? This turns familiar…
We present a new method of estimating the dispersion of a distribution which is based on the surprising property of a function that measures information processing intensity. It turns out that this function has a maximum at its fixed point.…
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent…
We study multivariate problems like function approximation, numerical integration, global optimization and dispersion. We obtain new results on the information complexity $n(\varepsilon,d)$ of these problems. The information complexity is…
Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be…
Rate-distortion-perception theory generalizes Shannon's rate-distortion theory by introducing a constraint on the perceptual quality of the output. The perception constraint complements the conventional distortion constraint and aims to…
We study the dispersion problem in anonymous port-labeled graphs: $k \leq n$ mobile agents, each with a unique ID and initially located arbitrarily on the nodes of an $n$-node graph with maximum degree $\Delta$, must autonomously relocate…
We give a high precision polynomial-time approximation scheme for the supremum of any honest n-variate (n+2)-nomial with a constant term, allowing real exponents as well as real coefficients. Our complexity bounds count field operations and…
In coding and information theory, it is desirable to construct maximal codes that can be either variable length codes or error control codes of fixed length. However deciding code maximality boils down to deciding whether a given NFA is…
We consider a communication system in which the outputs of a Markov source are encoded and decoded in \emph{real-time} by a finite memory receiver, and the distortion measure does not tolerate delays. The objective is to choose designs,…
The network communication scenario where one or more receivers request all the information transmitted by different sources is considered. We introduce distributed polynomial-time network codes in the presence of malicious nodes. Our codes…
This paper shows the strong converse and the dispersion of memoryless channels with cost constraints and performs refined analysis of the third order term in the asymptotic expansion of the maximum achievable channel coding rate, showing…
Shaping codes are used to encode information for use on channels with cost constraints. Applications include data transmission with a power constraint and, more recently, data storage on flash memories with a constraint on memory cell wear.…
An information-spectrum approach is applied to solve the multiterminal source coding problem for correlated general sources, where sources may be nonstationary and/or nonergodic, and the distortion measure is arbitrary and may be…
This paper explores the computational complexity of diffusion-based language modeling. We prove a dichotomy based on the quality of the score-matching network in a diffusion model. In one direction, a network that exactly computes the score…
Consider a team of $k \leq n$ autonomous mobile robots initially placed at a node of an arbitrary graph $G$ with $n$ nodes. The dispersion problem asks for a distributed algorithm that allows the robots to reach a configuration in which…
An intuitive outer bound for the multiterminal source coding problem is given. The proposed bound explicitly couples the rate distortion functions for each source and correlation measures which derive from a "strong" data processing…
We approach index coding as a special case of rate-distortion with multiple receivers, each with some side information about the source. Specifically, using techniques developed for the rate-distortion problem, we provide two upper bounds…
We study a delay-sensitive information flow problem where a source streams information to a sink over a directed graph G(V,E) at a fixed rate R possibly using multiple paths to minimize the maximum end-to-end delay, denoted as the…