Channel capacity and state estimation for state-dependent Gaussian channels

• Published in: IEEE transactions on information theory Vol. 51; no. 4; pp. 1486 - 1495
• Main Authors: Sutivong, A., Mung Chiang, Cover, T.M., Young-Han Kim
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2005; Institute of Electrical and Electronics Engineers
• Subjects: Additive Gaussian noise channels; Additive noise; Applied sciences; Channel capacity; Channel estimation; Channels; channels with state information; Detection, estimation, filtering, equalization, prediction; Errors; Exact sciences and technology; Gaussian; Gaussian channels; Gaussian noise; Information theory; Information, signal and communications theory; Interference; joint source-channel coding; Monitoring; Signal and communications theory; Signal, noise; state amplification; State estimation; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Transmitters; Additive noise; channels with state information; Channel capacity; Joint source-channel coding; Gaussian channel; Additive Gaussian noise channels; state amplification; State estimation; Information transmission; Mean square error
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2005.844108

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/spl par/S/sup n/ - S/spl circ//sup n//spl par/ for a state-dependent additive Gaussian channel Y/sup n/ = X/sup n/ + S/sup n/ + Z/sup n/ with an independent and identically distributed (i.i.d.) Gaussian state sequence S/sup n/ = (S/sub 1/, ..., S/sub n/) known at the transmitter and an unknown i.i.d. additive Gaussian noise Z/sup n/. We show that a simple technique of direct state amplification (i.e., X/sup n/ = /spl alpha/S/sup n/), 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.