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IEEE International Symposium on Information Theory (ISIT)

On the limits of communication over optical on-off keying channels with crosstalk

Hongchao Zhou, Gregory W. Wornell

Published Jun 1, 2014• 0 citations
Publisher

Abstract

In this paper, we investigate the limits of communication over optical on-off-keying channels with 1-D or 2-D crosstalk, where photons are transferable between adjacent time slots or spatial pixels, and the receiver is equipped with single-photon detectors.We observe that high transmission power (measured by the expected number of photons emitted in each signal slot or pixel) may not lead to high information rate; the maximum capacity is typically achieved in a low-photon regime - with about expected 3 to 8 photons received in each signal slot or pixel. Furthermore, we study the selection of slot length for maximizing the channel bandwidth, as the slot length affects the crosstalk probability and hence the channel capacity. It reveals that optimum optical-communication systems do not minimize the level of crosstalk between slots or pixels.

DOI
10.1109/isit.2014.6875346

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In this paper, we investigate the limits of communication over optical on-off-keying channels with 1-D or 2-D crosstalk, where photons are transferable between adjacent time slots or spatial pixels, and the receiver is equipped with single-photon detectors.We observe that high transmission power (measured by the expected number of photons emitted in each signal slot or pixel) may not lead to high information rate; the maximum capacity is typically achieved in a low-photon regime - with about expected 3 to 8 photons received in each signal slot or pixel. Furthermore, we study the selection of slot length for maximizing the channel bandwidth, as the slot length affects the crosstalk probability and hence the channel capacity. It reveals that optimum optical-communication systems do not minimize the level of crosstalk between slots or pixels.
The ability to transmit information from one point to another using as low received power as possible has a fundamental impact in many contexts, including covert communication, energy-efficient networks, and communication over channels with extreme loss. An immediate application is deep-space exploration, in which there has been significant interest in moving from microwaves to optical signals due to considerably lower diffraction loss and larger bandwidth. At a given data rate and transmit power, systems with the highest photon information efficiency (PIE), defined as the number of information bits extracted per received photon, can bridge the largest loss. We report here an experimental demonstration, using large-order pulse-position modulation and superconducting single-photon detectors, of a record PIE of 14.5 (17.8) bits per incident (detected) photon after 87.5dB of channel loss. This corresponds to 8.84 zeptojoules, or 0.069 photons, per bit at 1550nm. The record result was achieved using a new low-complexity transmitter design that produces short optical pulses on-demand with an average extinction ratio exceeding 90dB per time slot. To our knowledge, this is the most sensitive optical detection system ever demonstrated for high-path-loss optical communication.
The information capacity of an optical channel under power constraints is ultimately limited by the quantum nature of transmitted signals. We discuss currently available and emerging photonic technologies whose combination can be shown theoretically to enable nearly quantum-limited operation of a noisy optical communication link in the photon-starved regime, with the information rate scaling linearly in the detected signal power. The key ingredients are quantum pulse gating to facilitate mode selectivity, photon-number-resolved direct detection, and a photon-efficient high-order modulation format such as pulse position modulation, frequency shift keying, or binary phase shift keyed Hadamard words decoded optically using structured receivers.
Several methods have been proposed for the generation of photon-number-squeezed (sub-Poisson) light by imparting to the photon stream and anticorrelation that regularizes the times of arrival of the photons. This is accomplished by means of control of the excitation or emission process or by feedback, using a copy of the photon point processes when the emissions occur in parts. Possible advantages of communication by photon-number-squeezed light are discussed. For receivers in which the photon arrival times are observed, the channel capacity cannot be improved by modifying an initially Poisson photon stream and making it sub-Poisson. For photon-counting receivers, however, improvement of the channel capacity is possible. The bit-error-rate of an on-off keying communication system using sub-Poisson photons created by introducing anticorrelation into an initially Poisson beam may or may not be smaller than the error rates of the Poisson channel, depending on where the maximum power constraint is placed.>
It is well known that ideal free-space optical communication at the quantum limit can have unbounded photon information efficiency (PIE), measured in bits per photon. High PIE comes at a price of low dimensional information efficiency (DIE), measured in bits per spatio-temporal-polarization mode. If only temporal modes are used, then DIE translates directly to bandwidth efficiency. In this paper, the DIE vs. PIE tradeoffs for known modulations and receiver structures are compared to the ultimate quantum limit, and analytic approximations are found in the limit of high PIE. This analysis shows that known structures fall short of the maximum attainable DIE by a factor that increases linearly with PIE for high PIE. The capacity of the Dolinar receiver is derived for binary coherent-state modulations and computed for the case of on off keying (OOK). The DIE vs. PIE tradeoff for this case is improved only slightly compared to OOK with photon counting. An adaptive rule is derived for an additive local oscillator that maximizes the mutual information between a receiver and a transmitter that selects from a set of coherent states. For binary phase-shift keying (BPSK), this is shown to be equivalent to the operation of the Dolinar receiver. The Dolinar receiver is extended to make adaptive measurements on a coded sequence of coherent state symbols. Information from previous measurements is used to adjust the a priori probabilities of the next symbols. The adaptive Dolinar receiver does not improve the DIE vs. PIE tradeoff compared to independent transmission and Dolinar reception of each symbol.
The fundamental performance limits and channel capacity of optical communications systems operating over the free space channel will be examined using quantum detection theory. The performance of the optimum quantum receiver for on-off keying (OOK) and optical binary phase shift keying (BPSK) is first examined as a pure state (no noise) problem. The classical capacity of the binary symmetric channel for these two modulation schemes is then evaluated for the optimum quantum receiver by making use of the concept of quantum measurement states. The performance of M-ary pulse position modulation, which requires a product state representation, is evaluated along with the performance of certain 'dense signal sets.' Performance comparisons with classical techniques shows over 5 dB improvement in some cases when quantum detection is employed. As a further application of the quantum detection theory, the capacity of the binary channel with on-off keyed modulation and quantum detection is evaluated, and shown to exceed the capacity obtained with classical photon counting.
The process of attenuation of electromagnetic energy when transmitted over some communication channel is stochastic in nature. Hence one can expect that, since equivocation is imposed in the transmission, in addition to reduction of average signal power, there will be a consequent degradation in channel capacity. We have attempted to calculate the effect of this phenomenon on an otherwise noiseless photon channel and when the source itself is assumed to have no undesired fluctuations. In order to do so, we have employed a straightforward variational technique and introduced the partition function method of statistical mechanics to obtain an expression for channel capacity. Using approximate methods, we find that the maximum information transfer is achieved when the probability of receiving exactlykphotons goes down, asymptotically with largek, ase^{-ck}/ \sqrt{k}, wherecis a positive constant. For very large received average energyU(in photon number), the channel capacity behaves approximately asC = \frac{1}{2} \ln U, one-half the capacity of an ideal noiseless photon channel (given by Gordon's formula for the capacity of an electromagnetic wave). For very small received average energy, we find that the (optimum) received distribution is very nearly Bose-Einstein, and the channel capacity is not degraded below its ideal value. The results are applicable to an idealized laser oscillator and also to photoelectric detection. That is, both devices by themselves may be regarded as "channels" for which the input may be modulated as desired and the output is stochastically dependent on the input.