Rate Distortion Function in the Spin Glass State: A Toy Model
Tatsuto Murayama, Masato Okada · arXiv (Cornell University) · 2002
We applied statistical mechanics to an inverse problem of linear mapping to investigate the physics of optimal lossy compressions. We used the replica symmetry breaking technique with a toy model to demonstrate Shannon’s result. The rate distortion function, which is widely known as the theoretical limit of the compression with a fidelity criterion, is derived. Numerical study shows that sparse constructions of the model provide suboptimal compressions. 1