Channel capacity and state estimation for state-dependent Gaussian channels

Arak Sutivong, Mung Chiang, Thomas M. Cover, Young Han Kim

Research output: Contribution to journalArticle

74 Scopus citations

Abstract

We formulate a problem of state information transmission over a state-dependent channel with states known at the transmitter. In particular, we solve a problem of minimizing the mean-squared channel state estimation error E∥Sn - Ŝn∥ for a state-dependent additive Gaussian channel Yn = Xn + Sn + Zn with an independent and identically distributed (i.i.d.) Gaussian state sequence Sn = (S1,..., Sn) known at the transmitter and an unknown i.i.d. additive Gaussian noise Zn. We show that a simple technique of direct state amplification (i.e., Xn = αSn), where the transmitter uses its entire power budget to amplify the channel state, yields the minimum mean-squared state estimation error. This same channel can also be used to send additional independent information at the expense of a higher channel state estimation error. We characterize the optimal tradeoff between the rate R of the independent information that can be reliably transmitted and the mean-squared state estimation error D. We show that any optimal (R, D) tradeoff pair can be achieved via a simple power-sharing technique, whereby the transmitter power is appropriately allocated between pure information transmission and state amplification.

Original languageEnglish (US)
Pages (from-to)1486-1495
Number of pages10
JournalIEEE Transactions on Information Theory
Volume51
Issue number4
DOIs
StatePublished - Apr 1 2005

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

Keywords

  • Additive Gaussian noise channels
  • Channels with state information
  • Joint source-channel coding
  • State amplification
  • State estimation

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