On the Optimal Input of the Nondispersive Optical Fiber

The per-sample zero-dispersion channel model of the optical fiber is considered. It is shown that capacity is uniquely achieved by an input probability distribution that has continuous uniform phase and discrete amplitude that takes on finitely many values. This result holds when the channel is subject to general input cost constraints, that include a peak amplitude constraint and a joint average and peak amplitude constraint.

[1]  Ibrahim C. Abou-Faycal,et al.  Using Hermite Bases in Studying Capacity-Achieving Distributions Over AWGN Channels , 2012, IEEE Transactions on Information Theory.

[2]  Jihad Fahs,et al.  Capacity-Achieving Input Distribution in Per-Sample Zero-Dispersion Model of Optical Fiber , 2021, IEEE Transactions on Information Theory.

[3]  Frank R. Kschischang,et al.  Upper bound on the capacity of a cascade of nonlinear and noisy channels , 2015, 2015 IEEE Information Theory Workshop (ITW).

[4]  W. Rudin.  Principles of mathematical analysis , 1964 .

[5]  Frank R. Kschischang,et al.  On the Per-Sample Capacity of Nondispersive Optical Fibers , 2011, IEEE Transactions on Information Theory.

[6]  K. Turitsyn,et al.  Information capacity of optical fiber channels with zero average dispersion. , 2003, Physical review letters.

[7]  Shlomo Shamai,et al.  On the capacity-achieving distribution of the discrete-time noncoherent and partially coherent AWGN channels , 2004, IEEE Transactions on Information Theory.

[8]  Jihad Fahs,et al.  On the Finiteness of the Capacity of Continuous Channels , 2016, IEEE Transactions on Communications.

[9]  Joel G. Smith,et al.  The Information Capacity of Amplitude- and Variance-Constrained Scalar Gaussian Channels , 1971, Inf. Control..

[10]  Aslan Tchamkerten,et al.  On the discreteness of capacity-achieving distributions , 2004, IEEE Transactions on Information Theory.

[11]  H. Vincent Poor,et al.  The noncoherent rician fading Channel-part I: structure of the capacity-achieving input , 2005, IEEE Transactions on Wireless Communications.

[12]  M. Abramowitz,et al.  Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55) , 1965 .

[13]  Jihad Fahs,et al.  On Properties of the Support of Capacity-Achieving Distributions for Additive Noise Channel Models With Input Cost Constraints , 2016, IEEE Transactions on Information Theory.

[14]  Shlomo Shamai,et al.  The capacity of average and peak-power-limited quadrature Gaussian channels , 1995, IEEE Trans. Inf. Theory.