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

TL;DR

This paper decomposes mutual information in complex Gaussian channels into amplitude, phase, and mixed components, providing analytical insights at high SNR and applying the method to fiber-optic channels to explain spectral loss effects.

Contribution

It introduces a novel decomposition of mutual information into four parts for complex channels and applies it to analyze spectral loss in nonlinear fiber-optic channels.

Findings

Amplitude and phase dominate at high SNR.

Analytical expressions derived for Gaussian inputs at high SNR.

Spectral loss impacts capacity in nonlinear fiber-optic channels.

Abstract

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 presented in recent studies.