One step RSB scheme for the rate distortion function

TL;DR

This paper uses statistical mechanics and replica symmetry breaking to derive the rate distortion function, revealing limitations in achieving optimal compression in sparse systems.

Contribution

It introduces a novel application of the Parisi one step RSB scheme to derive the rate distortion function for linear mappings.

Findings

Derived the rate distortion function using RSB techniques

Showed the bound cannot be achieved in sparse systems

Identified dominance of suboptimal solutions in capacity

Abstract

We apply statistical mechanics to an inverse problem of linear mapping to investigate the physics of the irreversible compression. We use the replica symmetry breaking (RSB) technique with a toy model to demonstrate the Shannon's result. The rate distortion function, which is widely known as the theoretical limit of the compression with a fidelity criterion, is derived using the Parisi one step RSB scheme. The bound can not be achieved in the sparsely-connected systems, where suboptimal solutions dominate the capacity.