Citation
Abstract
We give a brief summary of the classical information capacity of single-mode free-space optical communication, both for pure-loss channels (i.e., with no background radiation), and for thermal-noise channels (i.e., with background radiation). We compare the capacities afforded by structured transmitters and receivers to that of the ultimate communication capacity. The ultimate capacity-achieving optical states are classical coherent states (i.e., ideal laser light), but the capacity-achieving receiver is yet to be determined. In addition, in photon-starved pure-loss channels, binary phase modulation in combination with the optimal receiver is near-capacity achieving, and more importantly, it is superior to on-off keying. In a pure-loss channel, heterodyne detection is near-optimal at high signal levels. In thermal-noise channels with high background noise and low signal we find that homodyne and heterodyne detection both approach the ultimate capacity, and at high signal heterodyne detection remains near-optimal. Finally, we quantify the degradation in channel capacity that is due to multiple noise modes contributing to the output of photon-counters. Electromagnetic waves are fundamentally quantized, and they are governed by the laws of quantum mechanics [1, 2]. This quantized nature has long been observed at optical frequencies through high-sensitivity photodetection systems. Therefore, when optical fields are the physical information carrier in a communication link, the ultimate rate of reliable communication is dictated by noise sources of quantum mechanical origin. A fundamental premise of quantum mechanics, which distinguishes it from classical mechanics, is that the outcome of a measurement on an electromagnetic field is probabilistic, and the statistics of the outcome are determined both by the measurement performed, and the state of the electromagnetic field at the time of the measurement [3]. As a consequence, the rate of reliable communication is impacted by both the alphabet of optical states used to convey information, and the measurement at the receiver to extract this information from the information carrier. In this article we address the capacity of a point-to-point communication channel utilizing optical fields as the physical information carrier. The mathematical framework that facilitates the analysis is (classical and quantum) information theory and random coding theorems: namely Shannon’s channel capacity theorem [4], and its quantum mechanical analog, the Holevo-Schumacher-Westmoreland (HSW) theorem [3]. A comprehensive survey of channel capacity results, with various technology-driven modulations, and using both classical and quantum receivers, has been reported in the recent literature [5, 6, 7, 8]. Our aim here is to complement this body of work by providing a summary of more recent results for single-mode free-space optical communication. We omit the derivations for brevity, and attempt to emphasize various avenues of future research that will enable communication at the ultimate rates dictated by quantum mechanics. This article is organized as follows. We begin with a brief review of the fundamentals in Section I. In particular, we review the classical and quantum channel capacity theorems based on random coding, and the normal-mode decomposition of the free-space propagation channel, which justifies the concept of single-mode operation. We have organized the material such that during the first reading this section may be skipped with no loss in continuity. We review in Section II the capacity of the pure-loss propagation channel, and in Section III the capacity of a channel with background noise coupled in from the environment. In Section IV, we derive the asymptotic expressions for the ultimate channel capacity with and without background noise. The degradation due to multiple noise modes contributing to photon counting is considered in Section V. Finally, in Section VI we present conclusions derived from our summary, emphasizing potentially fruitful avenues for research and development to approach the ultimate channel capacity of free-space optical communication.
Keywords
Details
- Volume
- 42-179
- Published
- November 15, 2009
- Pages
- 1–30
- File Size
- 393.8 KB