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Channel capacity and state estimation for state-dependent Gaussian channels

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4 Author(s)
A. Sutivong ; Dept. of Electr. Eng., Stanford Univ., CA, USA ; Mung Chiang ; T. M. Cover ; Young-Han Kim

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 - Sˆn|| 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.

Published in:

IEEE Transactions on Information Theory  (Volume:51 ,  Issue: 4 )