On the statistical physics of directed polymers in a random medium and their relation to tree codes

TL;DR

This paper applies statistical physics results to demonstrate that random tree codes can almost surely achieve the optimal distortion-rate function under specific symmetry conditions.

Contribution

It establishes a rigorous link between directed polymers in random media and the performance of random tree codes in data compression.

Findings

Random tree codes achieve the distortion-rate function almost surely.

The proof relies on properties of the free energy of directed polymers.

A symmetry condition is necessary for the result.

Abstract

Using well-known results from statistical physics, concerning the almost-sure behavior of the free energy of directed polymers in a random medium, we prove that random tree codes achieve the distortion-rate function almost surely under a certain symmetry condition.