Title :
On the heat channel and its capacity
Author :
Hammerich, Edwin
Author_Institution :
Minist. of Defence, Hof, Germany
fDate :
June 28 2009-July 3 2009
Abstract :
The heat channel is defined by an analog filter and a subsequent inaccurate measurement of the filter output signal. The filter is related to the solution of the heat equation and to the heat kernel of the quantum mechanical harmonic oscillator, so the name of the channel. The channel is modeled as an infinite-dimensional vector Gaussian channel and the capacity in terms of average energy of the input signal is derived. The relation to rate distortion theory is investigated by calculating the rate distortion function of a closely connected Gaussian process. Then a second formula for the capacity of the heat channel based on average energy of the measured filter output signal is given. The result is interpreted in context of estimation theory and a parallel to a famous formula connecting mutual information with minimum mean-square error in Gaussian channels is presented.
Keywords :
Gaussian processes; channel capacity; filtering theory; harmonic oscillators (circuits); mean square error methods; rate distortion theory; Gaussian process; analog filter; channel capacity; filter output signal measurement; heat channel; heat equation; infinite-dimensional vector Gaussian channel; minimum mean-square error method; quantum mechanical harmonic oscillator; rate distortion theory; Channel capacity; Equations; Gaussian channels; Gaussian processes; Kernel; Oscillators; Power harmonic filters; Quantum mechanics; Rate distortion theory; Rate-distortion;
Conference_Titel :
Information Theory, 2009. ISIT 2009. IEEE International Symposium on
Conference_Location :
Seoul
Print_ISBN :
978-1-4244-4312-3
Electronic_ISBN :
978-1-4244-4313-0
DOI :
10.1109/ISIT.2009.5205333
