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Conference Papers Year : 2023

Optimal Zero-Error Coding for Computing under Pairwise Shared Side Information

Abstract

We study the zero-error source coding problem in which an encoder with Side Information (SI) $g(Y)$ transmits source symbols $X$ to a decoder. The decoder has SI $Y$ and wants to recover $f(X,Y)$ where $f,g$ are deterministic. We exhibit a condition on the source distribution and $g$ that we call ``pairwise shared side information'', such that the optimal rate has a single-letter expression. This condition is satisfied if every pair of source symbols ``share" at least one SI symbol for all output of $g$; in the case $f(X,Y) = X$, the $P_{X,Y}$ and $g$ that satisfy it, induce the worst optimal rate. More generally for all $f$, it has a practical interpretation, as $Y$ models a request made by the encoder on an image $X$, and $g(Y)$ corresponds to the type of request. It also has a graph-theoretical interpretation: under ``pairwise shared side information'' the characteristic graph can be written as a disjoint union of OR products. In the case where the source distribution is full-support, we provide an analytic expression for the optimal rate. We develop an example under ``pairwise shared side information'', and we show that the optimal coding scheme outperforms several strategies from the literature.
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Dates and versions

hal-03901563 , version 1 (15-12-2022)
hal-03901563 , version 2 (19-06-2023)

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  • HAL Id : hal-03901563 , version 2

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Nicolas Charpenay, Maël Le Treust, Aline Roumy. Optimal Zero-Error Coding for Computing under Pairwise Shared Side Information. ITW 2023 - Information Theory Workshop, Apr 2023, Saint Malo, France. pp.1-5. ⟨hal-03901563v2⟩
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