## Abstract

Consider two correlated sources X and Y generated from a joint distribution pX,Y . Their Gács-Körner Common Information, a measure of common information that exploits the combinatorial structure of the distribution pX,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 Gács-Körner optimization. We then discuss properties of this optimization, and provide connections with the maximal correlation coefficient, as well as an efficient algorithm, both through the application of spectral graph theory to the induced bipartite graph of pX,Y .

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 Gács-Körner optimization. We then discuss properties of this optimization, and provide connections with the maximal correlation coefficient, as well as an efficient algorithm, both through the application of spectral graph theory to the induced bipartite graph of pX,Y .

Original language | English |
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Volume | abs/1604.03877 |

State | Published - 2016 |

### Publication series

Name | CoRR |
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