Gaussian channels with minimum amplitude constraints: When is optimal input binary?

In this paper, we consider a scalar Gaussian Channel with minimum amplitude constraint, and investigate when the capacity-achieving input is binary. First, we study the case that the input satisfies both minimum and peak amplitude constraints and find that the optimal input is discrete. Then, for a given minimum amplitude, we find sufficient conditions that the peak amplitude constraint must satisfy such that the optimal input is binary and when it is not binary. Similarly, for a given peak amplitude, we find sufficient conditions that the minimum amplitude constraint must satisfy such that the optimal input is binary and when it is not binary. Finally, we find that when the input satisfies minimum amplitude and average power constraints, the optimal input is not binary, regardless of whether there is also a peak amplitude constraint.

[1]  A. V. Arkhangel’skiǐ,et al.  The Basic Concepts and Constructions of General Topology , 1990 .

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

[3]  Lav R. Varshney,et al.  Transporting information and energy simultaneously , 2008, 2008 IEEE International Symposium on Information Theory.

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

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

[6]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[7]  M. Raginsky,et al.  On the information capacity of Gaussian channels under small peak power constraints , 2008, 2008 46th Annual Allerton Conference on Communication, Control, and Computing.

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

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

[10]  Ibrahim C. Abou-Faycal,et al.  The capacity of discrete-time memoryless Rayleigh-fading channels , 2001, IEEE Trans. Inf. Theory.

[11]  Mehul Motani,et al.  Subblock-Constrained Codes for Real-Time Simultaneous Energy and Information Transfer , 2015, IEEE Transactions on Information Theory.

[12]  M. Loève.  Probability theory : foundations, random sequences , 1955 .

[13]  S. Shamai,et al.  Characterizing the discrete capacity achieving distribution with peak power constraint at the transition points , 2008, 2008 International Symposium on Information Theory and Its Applications.