One step RSB scheme for the rate distortion function

Details One step RSB scheme for the rate distortion function One step RSB scheme for the rate distortion function

2002-07-26

arxiv.org/abs/cond-mat/0207637v8

Physics

Condensed Matter

Disordered Systems and Neural Networks

8 pages, 2 figures

Scientific paper

10.1088/0305-4470/36/43/031

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.

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