We study the fundamental limits of covert communications over general memoryless additive-noise channels. We assume that the legitimate receiver and the eavesdropper share the same channel and therefore see the same outputs. Under mild integrability assumptions, we find a general upper bound on the square-root scaling constant, which only involves the variance of the logarithm of the probability density function of the noise. Furthermore, we show that, under some additional assumptions, this upper bound is tight. We also provide upper bounds on the length of the secret key required to achieve the optimal scaling.

Consider the problem of distributed binary hypothesis testing with two terminals, where the decision is made at one of them (the “receiver”). We study the exponent of the error probability of the second type. Previously, an achievable exponent was derived by Shimokawa, Han, and Amari using a “quantization and binning” scheme. We propose a simple modification on the receiver’s decision rule in this scheme to attain a better exponent.

The capacity of a state-dependent discrete memoryless channel is derived for the setting where a message-cognizant rate-limited helper observes the state sequence noncausally and provides its description to both encoder and decoder. Said capacity is not increased if the channel outputs are fed back to the encoder via a noiseless feedback link. The analogous capacity is derived for the Gaussian channel, where the state corresponds to the additive noise. In this setting the feedback link—while not increasing capacity—eliminates the need for the helper’s cognition of the transmitted message. Moreover, in this setting, the results on capacity also hold for the cutoff rate and the listsize capacity.

A formula is derived for the capacity of the Gaus-sian channel with a message-cognizant rate-limited helper that provides a noncausal description of the noise to the encoder and the decoder. This capacity is strictly larger than when the helper is message oblivious. It is shown that, in this setup, a feedback link from the receiver to the encoder does not increase capacity. However, in the presence of such a link, said capacity can be achieved even if the helper is oblivious to the transmitted message.

A memoryless state sequence governing the behavior of a memoryless state-dependent channel is to be described causally to an encoder wishing to communicate over said channel. Given the maximal-allowed description rate, we seek the description that maximizes the Shannon capacity. It is shown that the maximum need not be achieved by a memoryless (symbol-by-symbol) description. Such descriptions are, however, optimal when the receiver is cognizant of the state sequence or when the description is allowed to depend on the message. For other cases, a block-Markov scheme with backward decoding is proposed.

We consider communication over a state-dependent discrete memoryless channel subject to a constraint that the output sequence must be nearly independent of the state sequence. We consider both cases where the transmitter knows (causally or noncausally) and where it does not know the states. When it does not know the states, we show that capacity can increase when the encoder uses some source of randomness that is not shared with the decoder. We consider three different cases for the state sequence: where it is independent and identically distributed across channel uses, where it is quasi-static, and where it has memory but is not quasi-static. We present single-letter capacity formulas for most combinations of the above scenarios, and also provide some illustrative examples.

We extend previous results on covert communication over the additive white Gaussian noise channel to two other types of additive noise channels. The first is the Gaussian channel with memory, where the noise sequence is a Gaussian vector with an arbitrary invertible covariance matrix. We show that the fundamental limit for covert communication over such a channel is the same as over the channel with white, i.e., memoryless, Gaussian noise. The second type of channel we consider is one with memoryless generalized Gaussian noise. For such a channel we prove a general upper bound on the dominant term in the maximum number of nats that can be covertly communicated over n channel uses. When the shape parameter p of the generalized Gaussian noise distribution is in the interval (0,1], we also prove a matching lower bound.

Consider a multiple-input single-output system, where the nonnegative, peak-limited inputs ${X_1}, \ldots ,{X_{{n_{\text{T}}}}} \in [0,\mathcal{A}]$ are subject to first- and second-moment sum-constraints on all antennas. The paper characterizes all probability distributions that can be induced for the "channel image," which is given by the inner product of the input vector with a given channel vector. Key to this result is the description of input vectors that achieve a given deterministic channel image with the smallest energy, where "energy" of an input vector refers to a weighted sum of its one- and two-norms. Minimum-energy input vectors have an interesting structure: depending on the desired channel image, some of the weakest antennas are silenced, and the remaining antennas are chosen according to a shifted and amplitude-constrained beamforming rule.

We consider a problem of communication over a physically-degraded additive white Gaussian noise wiretap channel. A covertness constraint is imposed, which says that the output at the wiretapper must statistically resemble pure noise. Previous works have shown that the total amount of information that can be transmitted over n uses of the channel is proportional to n, but the communication schemes in those works are designed to transmit only one message of predetermined length. We propose a feedback-aided scheme that, at the cost of less-than-optimal message length, is easily extensible to transmitting multiple messages and an unbounded amount of information.

The paper presents upper and lower bounds on the per-sector degrees of freedom (DoF) of a sectorized hexagonal cellular model when neighboring base stations (BSs) can cooperate during at most Δ interaction rounds over rate-limited backhaul links. The lower bound is based on practically implementable beamforming and adapts the way BSs cooperate to the sectorization of the cells. It improves over the naive approach that ignores this sectorization in terms of the sum-rate, both at finite signal-to-noise ratio (SNR) and in the high-SNR limit. For moderate SNR, the new scheme improves also over an opportunistic cooperation strategy where each message is decoded based on the signals received at the three adjacent sectors with the best SNR. The upper bound is information-theoretic and holds for all possible coding schemes, including for example interference alignment with unlimited symbol extensions whose practical implementation currently seems out of reach. Lower and upper bounds show that the complexity constraint, imposed by limiting the number of interaction rounds Δ, indeed limits the largest achievable sum-rate and DoF. In particular, irrespective of the backhaul capacity μ, the per-sector DoF cannot exceed a threshold which depends on Δ.

This work addresses distributed binary hypothesis testing, where observations at two terminals are jointly Gaussian, each one standard, with two possible correlation coefficients. We assume that one of the terminals is colocated with the decision center, and focus on a single (Stein) error exponent. Rather than the traditional exponent that is defined with respect to the source blocklength, we assume the source data to be unlimited, and consider the error exponent as a function of the communication message length. We examine two different approaches, one by quantization and the other by sending the index of the maximum, and find them to yield the same exponent. We further find that binning improves upon both approaches in the same way. Finally we compare the obtained exponents to two upper bounds and determine the optimal exponent in some very special cases.

This paper studies the capacity of a general multiple-input multiple-output (MIMO) free-space optical intensity channel under a per-input-antenna peak-power constraint and a total average-power constraint over all input antennas. The focus is on the scenario with more transmit than receive antennas. In this scenario, different input vectors can yield identical distributions at the output, when they result in the same image vector under multiplication by the channel matrix. We first determine the most energy-efficient input vectors that attain each of these image vectors. Based on this, we derive an equivalent capacity expression in terms of the image vector, and establish new lower and upper bounds on the capacity of this channel. The bounds match when the signal-to-noise ratio (SNR) tends to infinity, establishing the high-SNR asymptotic capacity. We also characterize the low-SNR slope of the capacity of this channel.

This paper investigates the capacity of block fading optical intensity channels with more transmit than receive antennas under different assumptions on the transmitter's channel state information (CSI). Lower and upper bounds on the capacities are derived using the entropy power inequality (EP!) and a dual expression for capacity. Our lower bounds for perfect and partial CSI utilize a transmit-antenna cooperation strategy based on minimum-energy signaling, which we proposed recently. For perfect CSI, this lower bound matches the upper bound asymptotically in the high signal-to-noise ratio (SNR) regime. For imperfect CSI, our lower bound is close to its perfect-CSI counterpart.

Given a code used to send a message to two receivers through a degraded discrete memoryless broadcast channel (DM-BC), the sender wishes to alter the codewords to achieve the following goals: (i) the original broadcast communication continues to take place, possibly at the expense of a tolerable increase of the decoding error probability; and (ii) an additional covert message can be transmitted to the stronger receiver such that the weaker receiver cannot detect the existence of this message. The main results are: (a) feasibility of covert communications is proven by using a random coding argument for general DM-BCs; and (b) necessary conditions for establishing covert communications are described and an impossibility (converse) result is presented for a particular class of DM-BCs. Together, these results characterize the asymptotic fundamental limits of covert communications for this particular class of DM-BCs within an arbitrarily small gap.

Coding and testing schemes and the corresponding achievable type-II error exponents are presented for binary hypothesis testing over two-hop relay networks. The schemes are based on cascade source coding techniques and unanimous decision-forwarding, the latter meaning that a terminal decides on the null hypothesis only if all previous terminals have decided on the null hypothesis. If the observations at the transmitter, the relay, and the receiver form a Markov chain in this order, then, without loss in performance, the proposed cascade source code can be replaced by two independent point-to-point source codes, one for each hop. The decoupled scheme (combined with decision-forwarding) is shown to attain the optimal type-II error exponents for various instances of “testing against conditional independence.” The same decoupling is shown to be optimal also for some instances of “testing against independence,” when the observations at the transmitter, the receiver, and the relay form a Markov chain in this order and when the relay-to-receiver link is of sufficiently high rate. For completeness, this paper also presents an analysis of the Shimokawa-Han-Amari binning scheme for the point-to-point hypothesis testing setup.

This paper studies the continuous-time Poisson channel whose dark current is random and may change for every τ-second time interval, where the actual values of the dark current are known to the transmitter as channel-state information (CSI). !n the limit where τ tends to zero, the capacity gain provided by both causal and noncausal CSI is shown to vanish linearly with τ, so CSI at the transmitter provides almost no capacity improvement. The paper also considers a related problem of the state-dependent very noisy channel. !n the very noisy limit, the capacity gain provided by noncausal CSI is shown to be the same as that provided by causal CSI.

We analyze a physically degraded relay channel, in which the transmitter sends a covert message to the legitimate receiver with the help of a relay. Two wardens, who do not collude with each other, monitor communication from the transmitter and the relay, respectively, through two Discrete Memoryless Channels (DMCs) to detect the presence of a covert message. The objective of the transmitter is to deliver the covert message successfully to the receiver without exceeding the covertness threshold of either warden. We identify the optimal asymptotic scaling of message and key bits and the dependence of the covert throughput on the two covertness thresholds.

We consider the problem of communication over a continuous-time, infinite-bandwidth Poisson channel without peak-power constraint, but subject to a covertness constraint: the relative entropy between the output distributions when a codeword is transmitted and when no input is provided to the channel must tend to zero as total communication time grows large. We show that, under such a constraint, the capacity of this channel, in nats per second, is infinity.

This paper investigates the capacity of the multiple- input multiple-output free-space optical intensity channel under a per-input-antenna peak-power constraint and a total average-power constraint over all input antennas. Our work considers the setup with more transmit than receive antennas, and characterizes capacity as an alternative optimization problem over the distribution of the input vector times the channel matrix. This alternative capacity expression is then used to obtain upper and lower bounds on the capacity, which match asymptotically in the high signal-to-noise ratio regime.

We consider the problem of covert communication over a state-dependent channel, where the transmitter has causal or noncausal knowledge of the channel states. Here, covert means that a warden on the channel should observe similar statistics when the transmitter is sending a message and when it is not. When a sufficiently long secret key is shared between the transmitter and the receiver, we derive closed-form formulas for the maximum achievable covert communication rate (covert capacity) for discrete memoryless channels and, when the transmitter's channel-state information (CSI) is noncausal, for additive white Gaussian noise (AWGN) channels. For certain channel models, including the AWGN channel, we show that the covert capacity is positive with CSI at the transmitter, but is zero without CSI. We also derive lower bounds on the rate of the secret key that is needed for the transmitter and the receiver to achieve the covert capacity.

This paper derives upper and lower bounds on the capacity of the multiple-input single-output free-space optical intensity channel with signal-independent additive Gaussian noise subject to both an average-intensity and a peak-intensity constraint. In the limit where the signal-to-noise ratio (SNR) tends to infinity, the asymptotic capacity is specified, while in the limit where the SNR tends to zero, the exact slope of the capacity is given.

We consider the problem of covert communication over a state-dependent channel, where the transmitter has non-causal knowledge of the channel states. Here, “covert” means that the probability that a warden on the channel can detect the communication must be small. In contrast with traditional models without noncausal channel-state information at the transmitter, we show that covert communication can be possible with positive rate. We derive closed-form formulas for the maximum achievable covert communication rate (“covert capacity”) in this setting for discrete memoryless channels as well as additive white Gaussian noise channels. We also derive lower bounds on the rate of the secret key that is needed for the transmitter and the receiver to achieve the covert capacity.

This paper provides several asymptotic capacity results for the multiple-input multiple-output free-space optical intensity channel in the regime of high signal-to-noise ratio (SNR). For the case where the channel matrix has full column rank, the asymptotic capacity is derived assuming a peak-power constraint on each transmit antenna, or an average-power constraint on the total power across all transmit antennas, or both. For multiple-input and single-output channels, the asymptotic high-SNR capacity is derived when either only the total average power is constrained, or only the per-antenna peak power is constrained, or both but with the average-power constraint being sufficiently loose.

This paper derives a simple strong data processing inequality (DPI) for Poisson processes: after a Poisson process is passed through p-thinning - in which every arrival remains in the process with probability p and is erased otherwise, independently of the other points - the mutual information between the Poisson process and any other random variable is reduced to no more than p times its original value. This strong DPI is applied to prove tight converse bounds in several problems: a hypothesis test with communication constraints, a mutual information game, and a CEO problem.

This paper derives the asymptotic capacity for the multiple-input single-output free-space optical intensity channel in the regime of high signal-to-noise ratio (SNR). The asymptotic result is proven via upper and lower bounds on capacity at finite SNR.

Binary hypothesis testing over single and parallel cascade channels is considered where sensors communicate with dedicated relays, and these relays with a single final receiver. All relays as well as the final receiver decide on the binary hypothesis governing the joint probability distribution of the observations at the sensors, relays, and final receiver. The quantity of interest is the set of feasible type-II error exponents that allow for the type-I error probabilities to vanish asymptotically as the observation length increases. A coding scheme is proposed and the corresponding set of feasible type-II error exponents is analyzed by means of a modified Han-type analysis that can account for distributed decisions based on different codebooks and for nodes forwarding their decisions to other nodes. The obtained exponent region is optimal in some special cases.

This paper considers a continuous-time Poisson channel whose dark current varies with time. The actual values of the dark current are revealed to the transmitter as channel-state information (CSI), either causally or noncausally. It is shown that, in the limit where the coherence time of the dark current tends to zero, the improvement on capacity provided by both causal and noncausal CSI vanishes linearly with the coherence time.

This paper considers the problem of communication over a memoryless classical-quantum wiretap channel subject to the constraint that the eavesdropper on the channel should not be able to learn with high confidence whether the legitimate parties are using the channel to communicate or not. Specifically, the relative entropy between the output quantum states at the eavesdropper when a codeword is transmitted and when no input is provided must be sufficiently small. Extending earlier works, this paper proves the “square-root law” for a broad class of classical-quantum channels: the maximum amount of information that can be reliably and covertly transmitted over n uses of such a channel scales like √n. The scaling constant is also determined.

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.

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 source generates a point pattern consisting of a finite number of points in an interval. Based on a binary description of the point pattern, a reconstructor must produce a covering set that is guaranteed to contain the pattern. We study the optimal tradeoff (as the length of the interval tends to infinity) between the description length and the least average Lebesgue measure of the covering set. The tradeoff is established for point patterns that are generated by homogeneous and inhomogeneous Poisson processes. The homogeneous Poisson process is shown to be the most difficult to describe among all point patterns. We also study a Wyner-Ziv version of this problem, where some of the points in the pattern are revealed to the reconstructor but not to the encoder. We show that this scenario is as good as when they are revealed to both encoder and reconstructor. A connection between this problem and the queueing distortion is established via feedforward. Finally, we establish the aforementioned tradeoff when the covering set is allowed to miss some of the points in the pattern at a certain cost.

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 channel's “dark current” approaches zero proportionally with ε. Extending our previous work, we show that the influence of the dark current on channel capacity is mainly on the third-order term with respect to ε. We also show that pulse-position modulation with “soft-decision decoding” achieves data rates that accurately reflect such influence.

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.

In the above-referenced paper, typesetting errors caused mismatch between labels of schemes and subscripts in equations. Schemes S-3, S-4, and S-5 should be relabeled S-1, S-2, and S-3, respectively.

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 channel's dark current approaches zero proportionally with ε. 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.

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.

We derive the capacity region of the state-dependent semideterministic broadcast channel with noncausal state-information at the transmitter. In this broadcast channel one of the outputs 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 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 channel's “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.

A source generates a “point pattern” consisting of a finite number of points in an interval. Based on a binary description of the point pattern, a reconstructor must produce a “covering set” that is guaranteed to contain the pattern. We study the optimal trade-off (as the length of the interval tends to infinity) between the description length and the least average Lebesgue measure of the covering set. The trade-off is established for point patterns that are generated by a Poisson process. Such point patterns are shown to be the most difficult to describe. We also study a Wyner-Ziv version of this problem, where some of the points in the pattern are known to the reconstructor but not to the encoder. We show that this scenario is as good as when they are known to both encoder and reconstructor.

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 powerε, capacity scales likeεlog 1/εfor smallε. For a Poisson channel whose dark current is a nonzero constant, capacity scales, to within a constant, likeεlog log 1/ε for smallε.

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 ldquosmooth 0-divergencerdquo, which is a generalization of Renyi's 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 Verdu and Han.

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).

Discrete-time Rayleigh fading multiple-input multiple-output (MIMO) channels are considered, with no channel state information at the transmitter and receiver. The fading is assumed to be correlated in time and independent from antenna to antenna. Peak and average transmit power constraints are imposed, either on the sum over antennas, or on each individual antenna. In both cases, an upper bound and an asymptotic lower bound, as the signal-to-noise ratio approaches zero, on the channel capacity are presented. The limit of normalized capacity is identified under the sum power constraints, and, for a subclass of channels, for individual power constraints. These results carry over to a SISO channel with delay spread (i.e. frequency selective fading).