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arXiv · 1707.03619

A unified approach to source and message compression

Anurag Anshu·Rahul Jain·Naqueeb Ahmad Warsi
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Abstract

We study the problem of source and message compression in the one-shot setting for the point-to-point and multi-party scenarios (with and without side information). We derive achievability results for these tasks in a unified manner, using the techniques of convex-split, which was introduced in [Anshu,Devabathini and Jain 2014] and position-based decoding introduced in [Anshu, Jain and Warsi 2017], which in turn uses hypothesis testing between distributions. These results are in terms of smooth max divergence and smooth hypothesis testing divergence. As a by-product of the tasks studied in this work, we obtain several known source compression results (originally studied in the asymptotic and i.i.d. setting) in the one-shot case. One of our achievability results includes the problem of message compression with side information, originally studied in [Braverman and Rao 2011]. We show that both our result and the result in [Braverman and Rao 2011] are near optimal in the one-shot setting by proving a converse bound.

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Anurag Anshu, Rahul Jain, Naqueeb Ahmad Warsi. 2017-07-12. A unified approach to source and message compression. https://arxiv.org/abs/1707.03619

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