Side Information Design in Zero-Error Coding for Computing

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...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Vol. 26; no. 4; pp. 338 - 18
Main Authors: Charpenay, Nicolas, Le Treust, Maël, Roumy, Aline
Format: Journal Article
Language:English
Published: Switzerland MDPI AG 16.04.2024
MDPI
Subjects:
Algorithms
Coders
Codes
Coding
Computation
Computer Science
Error analysis
graph theory
Greedy algorithms
Hypotheses
Mathematical analysis
Polynomials
Random variables
source coding
Video compression
zero-error information theory
France
graph theory
zero-error information theory
source coding
ISSN:1099-4300, 1099-4300
Online Access:Get full text
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Summary: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.
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ISSN:1099-4300
1099-4300
DOI:10.3390/e26040338