Lattice Quantization With Side Information: Codes, Asymptotics, and Applications in Sensor Networks

  • Authors:
  • S. D. Servetto

  • Affiliations:
  • Sch. of Electr. & Comput. Eng., Cornell Univ., Ithaca, NY

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2007

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Abstract

In this paper, 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