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Calculation of Mutual Information for Partially Coherent Gaussian Channels With Applications to Fiber Optics

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5 Author(s)
Bernhard Goebel ; Institute for Communications Engineering, Technische Universität München, Munich, Germany ; RenĂ©-Jean Essiambre ; Gerhard Kramer ; Peter J. Winzer
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The mutual information between a complex-valued channel input and its complex-valued output is decomposed into four parts based on polar coordinates: an amplitude term, a phase term, and two mixed terms. Numerical results for the additive white Gaussian noise (AWGN) channel with various inputs show that, at high signal-to-noise ratio (SNR), the amplitude and phase terms dominate the mixed terms. For the AWGN channel with a Gaussian input, analytical expressions are derived for high SNR. The decomposition method is applied to partially coherent channels and a property of such channels called “spectral loss” is developed. Spectral loss occurs in nonlinear fiber-optic channels and it may be one effect that needs to be taken into account to explain the behavior of the capacity of nonlinear fiber-optic channels.

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IEEE Transactions on Information Theory  (Volume:57 ,  Issue: 9 )