Maximum Entropy Functions: Approximate Gacs-Korner for Distributed Compression Academic Article uri icon

abstract

  • Consider two correlated sources $ X $ and $ Y $ generated from a joint distribution $ p_ {X, Y} $. Their G\'acs-K\" orner Common Information, a measure of common information that exploits the combinatorial structure of the distribution $ p_ {X, Y} $, leads to a source decomposition that exhibits the latent common parts in $ X $ and $ Y $. Using this source decomposition we construct an efficient distributed compression scheme, which can be efficiently used in the network setting as well. Then, we relax the combinatorial conditions on the source distribution, which results in an efficient scheme with a helper node, which can be thought of as a front-end cache. This relaxation leads to an inherent trade-off between the rate of the helper and the rate reduction at the sources, which we capture by a notion of optimal decomposition. We formulate this as an approximate G\'acs-K\" orner optimization …

publication date

  • April 13, 2016