Year: 2024
Type: article
Abstract: We investigate the zero-error coding for computing problems with encoder side information. An encoder provides access to a source X and is furnished with side information g(Y). It communicates with a decoder that possesses side information Y and aims to retrieve f(X,Y) with zero probability of error, where f and g are assumed to be deterministic functions. In previous work, we determined a condition that yields an analytic expression for the optimal rate R*(g); in particular, it covers the case where PX,Y is full support. In this article, we review this result and study the side information design problem, which consists of finding the best trade-offs between the quality of the encoder’s side information g(Y) and R*(g). We construct two greedy algorithms that give an achievable set of points in the side information design problem, based on partition refining and coarsening. One of them runs in polynomial time.
Source: Entropy
DOI: 10.3390/e26040338
Authors: Nicolas Charpenay, Maël Le Treust, Aline Roumy
Institutions: Centre National de la Recherche Scientifique, Institut de recherche mathématique de Rennes, Université de Rennes, Institut national de recherche en sciences et technologies du numérique, Institut de Recherche en Informatique et Systèmes Aléatoires, Centre Inria de l'Université de Rennes
Language: English
Subfield: Theoretical Computer Science
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
Funder: Agence Nationale de la Recherche
Awards: G2014946915, G3343749973, G7240651115
OpenAlex ID: W4394847360