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 language | English (US) |
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Pages (from-to) | 1486-1495 |
Number of pages | 10 |
Journal | IEEE Transactions on Information Theory |
Volume | 51 |
Issue number | 4 |
DOIs | |
State | Published - 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