Upper Bound on the Joint Entropy of Correlated Sources Encoded by Good Lattices

Abstract

Lattices provide useful structure for distributed coding of correlated sources. A common lattice encoder construction is to first round an observed sequence to a `fine’ lattice with dither, then produce the result’s modulo to a `coarse’ lattice as the encoding. However, such encodings may be jointly-dependent. A class of upper bounds is established on the conditional entropy-rates of such encodings when sources are correlated and Gaussian and the lattices involved are a from an asymptotically-well-behaved sequence. These upper bounds guarantee existence of a joint–compression stage which can increase encoder efficiency. The bounds exploit the property that the amount of possible values for one encoding collapses when conditioned on other sufficiently informative encodings. The bounds are applied to the scenario of communicating through a many-help-one network in the presence of strong correlated Gaussian interferers, and such a joint–compression stage is seen to compensate for some of the inefficiency in certain simple encoder designs.