The Poisson Fading Channel

In this first paper of a two-part series, a single-user single-input single-output (SISO) shot-noise-limited Poisson channel is considered over which an information signal is transmitted by modulating the intensity of an optical beam, and individual photon arrivals are counted at the photodetector receiver. The transmitted signal, which is chosen to satisfy peak and average constraints, undergoes multiplicative fading, which occurs over coherence time intervals of fixed duration. The fade coefficient (channel state) remains constant in each coherence interval, and varies across successive such intervals in an independent and identically distributed (i.i.d.) fashion. A single-letter characterization of the capacity of this channel is obtained when the receiver is provided with perfect channel state information (CSI) while the transmitter CSI can be imperfect. The asymptotic behavior of channel capacity in the low and high peak-signal-to-shot-noise ratio (SNR) regimes is studied.

[1]  S. Clifford.  Wave Propagation in a Turbulent Medium. , 1969 .

[2]  Amiel Feinstein,et al.  Information and information stability of random variables and processes , 1964 .

[3]  Robert J. McEliece,et al.  Practical codes for photon communication , 1981, IEEE Trans. Inf. Theory.

[4]  Shane M. Haas,et al.  Capacity of and coding for multiple-aperture, wireless, optical communications , 2006 .

[5]  R. A. Silverman,et al.  Wave Propagation in a Turbulent Medium , 1961 .

[6]  Wayne E. Stark,et al.  Channels with block interference , 1984, IEEE Trans. Inf. Theory.

[7]  Muriel Médard,et al.  The effect upon channel capacity in wireless communications of perfect and imperfect knowledge of the channel , 2000, IEEE Trans. Inf. Theory.

[8]  J. Hamkins,et al.  Multipulse Pulse-Position Modulation on Discrete Memoryless Channels , 2005 .

[9]  K. Wilson,et al.  Preliminary analysis of fluctuations in the received uplink-beacon-power data obtained from the GOLD experiments , 1996 .

[10]  Isaac I. Kim,et al.  Scintillation reduction using multiple transmitters , 1997, Photonics West.

[11]  James R. Lesh,et al.  Capacity Limit of the Noiseless, Energy-Efficient Optical PPM Channel , 1983, IEEE Trans. Commun..

[12]  H. A. Willebrand,et al.  Fiber optics without fiber , 2001 .

[13]  Jeffrey H. Shapiro,et al.  Capacity of the multiple-input, multiple-output Poisson channel , 2002 .

[14]  R. G. Lipes.  Pulse-Position-Modulation Coding as Near-Optimum Utilization of Photon Counting Channel with Bandwidth and Power Constraints , 1980 .

[15]  Shlomo Shamai,et al.  Fading Channels: Information-Theoretic and Communication Aspects , 1998, IEEE Trans. Inf. Theory.

[16]  Shlomo Shamai.  On the capacity of a direct-detection photon channel with intertransition-constrained binary input , 1991, IEEE Trans. Inf. Theory.

[17]  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.

[18]  Shlomo Shamai,et al.  Bounds on the capacity of a spectrally constrained Poisson channel , 1993, IEEE Trans. Inf. Theory.

[19]  Gerard Lachs,et al.  Information rates for photocount detection systems , 1969, IEEE Trans. Inf. Theory.

[20]  Y. Kabanov.  The Capacity of a Channel of the Poisson Type , 1978 .

[21]  Akira Ishimaru,et al.  Wave propagation and scattering in random media , 1997 .

[22]  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.

[23]  John R. Pierce,et al.  The capacity of the photon counting channel , 1981, IEEE Trans. Inf. Theory.

[24]  M. Wright,et al.  Mountain-Top-to-Mountain-Top Optical Link Demonstration: Part I , 2002 .

[25]  S. Verdú.  Poisson Communication Theory , 2004 .

[26]  J. H. Shapiro.  Imaging and optical communication through atmospheric turbulence , 1978 .

[27]  Giuseppe Caire,et al.  Optimum power control over fading channels , 1999, IEEE Trans. Inf. Theory.

[28]  James R. Lesh,et al.  Bandwidth Limitations on Noiseless Optical Channel Capacity , 1982, IEEE Trans. Commun..

[29]  Shlomo Shamai,et al.  On the capacity of some channels with channel state information , 1999, IEEE Trans. Inf. Theory.

[30]  J. Pierce,et al.  Optical Channels: Practical Limits with Photon Counting , 1978, IEEE Trans. Commun..

[31]  Etty J. Lee,et al.  Part 1: optical communication over the clear turbulent atmospheric channel using diversity , 2004, IEEE Journal on Selected Areas in Communications.

[32]  Kaushik Chakraborty.  Capacity of the MIMO optical fading channel , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[33]  Jeffrey H. Shapiro,et al.  Capacity of wireless optical communications , 2003, IEEE J. Sel. Areas Commun..

[34]  Prakash Narayan,et al.  Capacities of time-varying multiple-access channels with side information , 2002, IEEE Trans. Inf. Theory.

[35]  Donald L. Snyder,et al.  Random Point Processes in Time and Space , 1991 .

[36]  Andrea J. Goldsmith,et al.  Capacity limits of MIMO channels , 2003, IEEE J. Sel. Areas Commun..

[37]  Vahid Tarokh,et al.  Space-Time Codes for Wireless Optical Communications , 2002, EURASIP J. Adv. Signal Process..

[38]  Israel Bar-David,et al.  Information in the time of arrival of a photon packet - Capacity of PPM channels. , 1973 .

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

[40]  S. Brendle,et al.  Calculus of Variations , 1927, Nature.