A refined analysis of the Poisson channel in the high-photon-efficiency regime

We study the discrete-time Poisson channel under the constraint that its average input power (in photons per channel use) must not exceed some constant E. We consider the wideband, high-photon-efficiency extreme where E approaches zero, and where the channel's "dark current" approaches zero proportionally with E. Improving over a previously obtained first-order capacity approximation, we derive a refined approximation, which includes the exact characterization of the second-order term, as well as an asymptotic characterization of the third-order term with respect to the dark current. We also show that pulse-position modulation is nearly optimal in this regime.Comment: Revised version to appear in IEEE Transactions on Information Theor

Structured Optical Receivers for Efficient Deep-Space Communication

We discuss conceptual designs for structured optical receivers that can alleviate the requirement for high peak-to-average power ratio in photon-starved optical communication. The basic idea is to transmit sequences of suitably modulated coherent light pulses whose energy can be concentrated in a single temporal bin on the receiver side through optical interference. Two examples of scalable architectures for structured receivers are presented. The first one, based on active polarization switching, maps Hadamard codewords composed from the binary phase shift keying (BPSK) constellation onto the standard pulse position modulation (PPM) format. The second receiver, using solely passive optical elements, converts phase-polarization patterns of coherent light pulses into a single pulse preserving a synchronized time of arrival. Such a conversion enables implementation of a communication protocol equivalent to the PPM scheme but with distributed optical power provided that the intersymbol guard-time exceeds the pattern length.Comment: 4 pages, 2 figures. To be presented at the IEEE International Conference on Space Optical Systems and Applications, 14-16 November 2017, Naha, Okinawa, Japa

Improved capacity upper bounds for the discrete-time poisson channel

We present new capacity upper bounds for the discrete-time Poisson channel with no dark current and an average-power constraint. These bounds are a simple consequence of techniques developed by one of the authors for the seemingly unrelated problem of upper bounding the capacity of binary deletion and repetition channels. Previously, the best known capacity upper bound in the regime where the average-power constraint does not approach zero was due to Martinez (JOSA B, 2007), which we re-derive as a special case of our framework. Furthermore, we instantiate our framework to obtain a closed-form bound that noticeably improves the result of Martinez everywhere

Toward Photon-Efficient Key Distribution over Optical Channels

This work considers the distribution of a secret key over an optical (bosonic) channel in the regime of high photon efficiency, i.e., when the number of secret key bits generated per detected photon is high. While in principle the photon efficiency is unbounded, there is an inherent tradeoff between this efficiency and the key generation rate (with respect to the channel bandwidth). We derive asymptotic expressions for the optimal generation rates in the photon-efficient limit, and propose schemes that approach these limits up to certain approximations. The schemes are practical, in the sense that they use coherent or temporally-entangled optical states and direct photodetection, all of which are reasonably easy to realize in practice, in conjunction with off-the-shelf classical codes.Comment: In IEEE Transactions on Information Theory; same version except that labels are corrected for Schemes S-1, S-2, and S-3, which appear as S-3, S-4, and S-5 in the Transaction

Coding against synchronisation and related errors

In this thesis, we study aspects of coding against synchronisation errors, such as deletions and replications, and related errors. Synchronisation errors are a source of fundamental open problems in information theory, because they introduce correlations between output symbols even when input symbols are independently distributed. We focus on random errors, and consider two complementary problems: We study the optimal rate of reliable information transmission through channels with synchronisation and related errors (the channel capacity). Unlike simpler error models, the capacity of such channels is unknown. We first consider the geometric sticky channel, which replicates input bits according to a geometric distribution. Previously, bounds on its capacity were known only via numerical methods, which do not aid our conceptual understanding of this quantity. We derive sharp analytical capacity upper bounds which approach, and sometimes surpass, numerical bounds. This opens the door to a mathematical treatment of its capacity. We consider also the geometric deletion channel, combining deletions and geometric replications. We derive analytical capacity upper bounds, and notably prove that the capacity is bounded away from the maximum when the deletion probability is small, meaning that this channel behaves differently than related well-studied channels in this regime. Finally, we adapt techniques developed to handle synchronisation errors to derive improved upper bounds and structural results on the capacity of the discrete-time Poisson channel, a model of optical communication. Motivated by portable DNA-based storage and trace reconstruction, we introduce and study the coded trace reconstruction problem, where the goal is to design efficiently encodable high-rate codes whose codewords can be efficiently reconstructed from few reads corrupted by deletions. Remarkably, we design such n-bit codes with rate 1-O(1/log n) that require exponentially fewer reads than average-case trace reconstruction algorithms.Open Acces