Year: 2023
Type: conference-paper
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 PX,Yand 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.
Authors: Nicolas Charpenay, Maël Le Treust, Aline Roumy
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4382365125