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.
Highlights
Lattice codes are a useful tool for information theoretic analysis of communications networks.Sequences of lattices can be designed to posess certain properties which make them useful for noisy channel coding or source coding in limit with dimension
Yang in [8] realized a similar compression scheme for such encodings using further lattice processing on them and presents an insightful ‘coset planes’ abstraction. It was further noticed by Yang in [9] that improvement towards the many-help-one problem is obtained by splitting helper messages into two parts: one part a coarse quantization of the signal, compressed across helpers via Slepian–Wolf joint–compression, and another a lattice-modulo-encoding representing signal details
The achievable rate given in Corollary 1 depends on the design of the lattice encoding scheme at the helpers
Summary
Lattice codes are a useful tool for information theoretic analysis of communications networks. Sequences of lattices can be designed to posess certain properties which make them useful for noisy channel coding or source coding in limit with dimension. These properties have been termed ‘good for channel coding’ and ‘good for source coding’ [1]. Well designed codes for such a scenario built off of such lattices enables encoders to produce a more efficient representation of their observations than would be possible without joint code design [3] Such codes can provide optimal or near-optimal solutions to coding problems [4,5,6]. The upper bound establishes stronger performance limits for such coding structures since it demonstrates that encoders are able to convey the same encodings at lower messaging rates
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