Ligong Wang

One-Shot Classical-Quantum Capacity and Hypothesis Testing

The one-shot classical capacity of a quantum channel quantifies the amount of classical information that can be transmitted through a single use of the channel such that the error probability is below a certain threshold. In this work, we show that this capacity is well approximated by a relative-entropy-type measure defined via hypothesis testing. Combined with a quantum version of Steins lemma, our results give a conceptually simple proof of the well-known Holevo-Schumacher-Westmoreland theorem for the capacity of memoryless channels. More generally, we obtain tight capacity formulas for arbitrary (not necessarily memoryless) channels.

Simple channel coding bounds

New channel coding converse and achievability bounds are derived for a single use of an arbitrary channel. Both bounds are expressed using a quantity called the “smooth 0-divergence”, which is a generalization of Rényis divergence of order 0. The bounds are also studied in the limit of large block-lengths. In particular, they combine to give a general capacity formula which is equivalent to the one derived by Verdú and Han.

Low-SNR Capacity of Noncoherent Fading Channels

Discrete-time Rayleigh-fading single-input single-output (SISO) and multiple-input multiple-output (MIMO) channels are considered, with no channel state information at the transmitter or the receiver. The fading is assumed to be stationary and correlated in time, but independent from antenna to antenna. Peak-power and average-power constraints are imposed on the transmit antennas. For MIMO channels, these constraints are either imposed on the sum over antennas, or on each individual antenna. For SISO channels and MIMO channels with sum power constraints, the asymptotic capacity as the peak signal-to-noise ratio (SNR) goes to zero is identified; for MIMO channels with individual power constraints, this asymptotic capacity is obtained for a class of channels called transmit separable channels. The results for MIMO channels with individual power constraints are carried over to SISO channels with delay spread (i.e., frequency-selective fading).

Fundamental Limits of Communication With Low Probability of Detection

This paper considers the problem of communication over a discrete memoryless channel (DMC) or an additive white Gaussian noise (AWGN) channel subject to the constraint that the probability that an adversary who observes the channel outputs can detect the communication is low. In particular, the relative entropy between the output distributions when a codeword is transmitted and when no input is provided to the channel must be sufficiently small. For a DMC whose output distribution induced by the “off” input symbol is not a mixture of the output distributions induced by other input symbols, it is shown that the maximum amount of information that can be transmitted under this criterion scales like the square root of the blocklength. The same is true for the AWGN channel. Exact expressions for the scaling constant are also derived.

The Discrete-Time Poisson Channel at Low Input Powers

The asymptotic capacity at low input powers of an average-power limited or an average- and peak-power limited discrete-time Poisson channel is considered. For a Poisson channel whose dark current is zero or decays to zero linearly with its average input power <i>ε</i>, capacity scales like <i>ε</i> log 1/<i>ε</i> for small <i>ε</i>. For a Poisson channel whose dark current is a nonzero constant, capacity scales, to within a constant, like <i>ε</i> log log 1/ε for small <i>ε</i>.

The State-Dependent Semideterministic Broadcast Channel

We derive the capacity region of the state-dependent semideterministic broadcast channel with noncausal state information at the transmitter. One of the two outputs of this channel is a deterministic function of the channel input and the channel state, and the state is assumed to be known noncausally to the transmitter but not to the receivers. We show that appending the state to the deterministic output does not increase capacity. We also derive an outer bound on the capacity of general (not necessarily semideterministic) state-dependent broadcast channels.

The Poisson channel with side information

The continuous-time, peak-limited, infinite-bandwidth Poisson channel with spurious counts is considered. It is shown that if the times at which the spurious counts occur are known noncausally to the transmitter but not to the receiver, then the capacity is equal to that of the Poisson channel with no spurious counts. Knowing the times at which the spurious counts occur only causally at the transmitter does not increase capacity.

Limits of low-probability-of-detection communication over a discrete memoryless channel

This paper considers the problem of communication over a discrete memoryless channel subject to the constraint that the probability that an adversary who observes the channel outputs can detect the communication is low. Specifically, the relative entropy between the output distributions when a codeword is transmitted and when no input is provided to the channel must be sufficiently small. For a channel whose output distribution induced by the zero input symbol is not a mixture of the output distributions induced by other input symbols, it is shown that the maximum number of bits that can be transmitted under this criterion scales like the square root of the blocklength. Exact expressions for the scaling constant are also derived.

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 ε. We consider the wideband, high-photon-efficiency extreme where ε approaches zero, and where the channels “dark current” approaches zero proportionally with ε. Improving over a previously obtained first-order capacity approximation, we derive a refined approximation which also includes the second-order term. We also show that pulse-position modulation is optimal on this channel up to the second-order term in capacity.

Toward Photon-Efficient Key Distribution Over Optical Channels

This paper 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.