Uncoded Transmission Is Exactly Optimal for a Simple Gaussian “Sensor” Network

  • Authors:
  • M. Gastpar

  • Affiliations:
  • Dept. of Electr. Eng. & Comput. Sci., Univ. of California, Berkeley, CA

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2008

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Abstract

A single memoryless Gaussian source is observed by many terminals, subject to independent Gaussian observation noises. The terminals are linked to a fusion center via a standard Gaussian multiple-access channel. The fusion center needs to recover the underlying Gaussian source with respect to mean-squared error. In this correspondence, a theorem of Witsenhausen is shown to imply that an optimal communication strategy is uncoded transmission, i.e., each terminal's channel input is merely a scaled version of its noisy observation.