Capacity Bounds for Wireless Optical Intensity Channels With Gaussian Noise

Lower and upper bounds on the capacity of wireless optical intensity pulse amplitude modulation channels under nonnegativity and average optical power constraints are derived. A lower bound is derived based on source entropy maximization over a family of discrete nonuniform distributions with equally spaced mass points. A closed form for the maxentropic discrete input distribution is provided. Compared to previously reported bounds, the derived lower bound is tight at both low and high signal-to-noise ratios (SNRs). In addition, a closed-form upper bound is derived based on signal space geometry via a sphere packing argument. The proposed bound is tight at low SNRs and incurs a small gap to the channel capacity at high SNRs. The derived bounds asymptotically describe the optical intensity channel capacity at low SNRs, where a majority of such links operate.

[1]  Per Ola Börjesson,et al.  Simple Approximations of the Error Function Q(x) for Communications Applications , 1979, IEEE Trans. Commun..

[2]  S. Shamai,et al.  Capacity of a pulse amplitude modulated direct detection photon channel , 1990 .

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

[4]  R. Nickalls.  A new approach to solving the cubic: Cardan’s solution revealed , 1993, The Mathematical Gazette.

[5]  Stefan M. Moser.  Duality-based bounds on channel capacity , 2005 .

[6]  Ulrich Betke,et al.  Intrinsic volumes and lattice points of crosspolytopes , 1993 .

[7]  Joseph M. Kahn,et al.  Upper-bounding the capacity of optical IM/DD Channels with multiple-subcarrier modulation and fixed bias using trigonometric moment space method , 2002, IEEE Trans. Inf. Theory.

[8]  C.E. Shannon,et al.  Communication in the Presence of Noise , 1949, Proceedings of the IRE.

[9]  Amos Lapidoth,et al.  On the Capacity of Free-Space Optical Intensity Channels , 2008, IEEE Transactions on Information Theory.

[10]  Frank R. Kschischang,et al.  Capacity bounds for power- and band-limited optical intensity channels corrupted by Gaussian noise , 2004, IEEE Transactions on Information Theory.

[11]  Frank R. Kschischang,et al.  Optical intensity-modulated direct detection channels: signal space and lattice codes , 2003, IEEE Trans. Inf. Theory.

[12]  L. Gordon.  A Stochastic Approach to the Gamma Function , 1994 .

[13]  Mark H. A. Davis,et al.  Capacity and cutoff rate for Poisson-type channels , 1980, IEEE Trans. Inf. Theory.

[14]  Frank R. Kschischang,et al.  Capacity-achieving probability measure for conditionally Gaussian channels with bounded inputs , 2005, IEEE Transactions on Information Theory.

[15]  Jeffrey B. Carruthers,et al.  Wireless infrared communications , 2003, Proc. IEEE.