## Spectral efficiency of optical direct detection

JOSA B, Vol. 24, Issue 4, pp. 739-749 (2007)

http://dx.doi.org/10.1364/JOSAB.24.000739

Enhanced HTML Acrobat PDF (174 KB)

### Abstract

The spectral efficiency (channel capacity) of the optical direct-detection channel is studied. The modeling of the optical direct-detection channel as a discrete-time Poisson channel is reviewed. Closed-form integral representations for the entropy of random variables with Poisson and negative binomial distributions are derived. The spectral efficiency achievable with an arbitrary input gamma density is expressed in closed integral form. Simple, nonasymptotic upper and lower bounds to the channel capacity are computed. Numerical results are presented and compared with previous bounds and approximations.

© 2007 Optical Society of America

**OCIS Codes**

(030.5260) Coherence and statistical optics : Photon counting

(060.4510) Fiber optics and optical communications : Optical communications

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: July 14, 2006

Revised Manuscript: November 7, 2006

Manuscript Accepted: November 7, 2006

Published: March 15, 2007

**Citation**

Alfonso Martinez, "Spectral efficiency of optical direct detection," J. Opt. Soc. Am. B **24**, 739-749 (2007)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-24-4-739

Sort: Year | Journal | Reset

### References

- R. G. Gallager, Information Theory and Reliable Communication (Wiley, 1968).
- C. M. Caves and P. D. Drummond, "Quantum limits on bosonic communication rates," Rev. Mod. Phys. 66, 481-537 (1994). [CrossRef]
- J. M. Kahn and K.-P. Ho, "Spectral efficiency limits and modulation/detection techniques for DWDM systems," IEEE J. Sel. Top. Quantum Electron. 10, 259-272 (2004). [CrossRef]
- J. P. Gordon, "Quantum effects in communication systems," Proc. IRE 50, 1898-1908 (1962). [CrossRef]
- S. Shamai (Shitz), "Capacity of a pulse amplitude modulated direct detection photon channel," IEE Proc., Part I: Solid-State Electron Devices 137, 424-430 (1990).
- D. Brady and S. Verdú, "The asymptotic capacity of the direct detection photon channel with a bandwidth constraint," in Proceedings of the 28th Annual Allerton Conference on Communication, Control, and Computing (Allerton, 1990), pp. 691-700.
- A. Lapidoth and S. M. Moser, "Bounds on the capacity of the discrete-time Poisson channel," in Proceedings of the 41st Allerton Conference on Communication, Control, and Computing, (Allerton, 2003), pp. 201-210.
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
- A. Peres, Quantum Theory: Concepts and Methods (Kluwer Academic, 1995).
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, 2000).
- M. Sargent III, M. O. Scully, and W. E. Lamb, Jr., Laser Physics (Addison-Wesley, 1974).
- G. E. Andrews, R. Askey, and R. Roy, Special Functions (Cambridge U. Press, 1999).
- W. Feller, An Introduction to Probability Theory and Its Applications, 2nd ed. (Wiley, 1971), Vol. 2.
- I. Csiszár and J. Körner, Information Theory: Coding Theorems for Discrete Memoryless Systems (Academic, 1981).
- R. E. Blahut, Principles and Practice of Information Theory (Addison-Wesley, 1987).
- I. C. Abou-Faycal, M. D. Trott, and S. Shamai (Shitz), "The capacity of discrete-time memoryless Rayleigh-fading channels," IEEE Trans. Inf. Theory 47, 1290-1301 (2001). [CrossRef]
- I.S.Gradshteyn, I.M.Ryzhik, and A.Jeffrey (eds.), Tables of Integrals, Series, and Products (Academic, 1994).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.