Lattice Quantization with Side Information: Codes, Asymptotics, and Applications in Sensor Networks
<|reference_start|>Lattice Quantization with Side Information: Codes, Asymptotics, and Applications in Sensor Networks: We consider the problem of rate/distortion with side information available only at the decoder. For the case of jointly-Gaussian source X and side information Y, and mean-squared error distortion, Wyner proved in 1976 that the rate/distortion function for this problem is identical to the conditional rate/distortion function R_{X|Y}, assuming the side information Y is available at the encoder. In this paper we construct a structured class of asymptotically optimal quantizers for this problem: under the assumption of high correlation between source X and side information Y, we show there exist quantizers within our class whose performance comes arbitrarily close to Wyner's bound. As an application illustrating the relevance of the high-correlation asymptotics, we also explore the use of these quantizers in the context of a problem of data compression for sensor networks, in a setup involving a large number of devices collecting highly correlated measurements within a confined area. An important feature of our formulation is that, although the per-node throughput of the network tends to zero as network size increases, so does the amount of information generated by each transmitter. This is a situation likely to be encountered often in practice, which allows us to cast under new--and more ``optimistic''--light some negative results on the transport capacity of large-scale wireless networks.<|reference_end|>
@article{servetto2006lattice,
    title={Lattice Quantization with Side Information: Codes, Asymptotics, and
  Applications in Sensor Networks},
    author={Sergio D. Servetto (Cornell University)},
    journal={IEEE Transactions on Information Theory; 53(2):714-731, 2007.},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0611002},
    primaryClass={cs.IT math.IT}
}