An Information-Theoretic Approach to Joint Sensing and Communication

The problem of constellation shaping for broadcast transmission in degraded channels remains a challenge. This is especially so when a single source communicates simultaneously with two receivers using a finite dimension constellation. This paper focuses on a practical situation where unicast service to each user is transmitted over broadcast channels. We investigate the optimization of an achievable rate closure region by using non-uniform constellations issued from superimposition of high-rate information on low-rate information and by using a nonequiprobable distribution of the transmitted symbols. The achievable rate region is derived for a two-user additive white Gaussian noise (AWGN) broadcast channel and for finite input pulse amplitude modulation (PAM) constellations. A noticeable shaping gain up to 3.5 dB maximum was shown on signal-to-noise ratio (SNR), compared with the equiprobable distribution of transmitted symbols obtained for a 4-PAM constellation when achievable rates are maximized over the probability distribution of channel input signals and the constellation shape. © 2012 Alcatel-Lucent.

In this paper, we consider a general K-user Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC). We assume that the channel state is deterministic and known to all the nodes. While the private-message capacity region is well known to be achievable with dirty paper coding (DPC), we are interested in the simpler linearly precoded transmission schemes. In particular, we focus on linear precoding schemes combined with rate-splitting (RS). First, we derive an achievable rate region with minimum mean square error (MMSE) precoding at the transmitter and joint decoding of the sub-messages at the receivers. Then, we study the achievable sum rate of this scheme and obtain two findings: 1) an analytically tractable upper bound on the sum rate that is shown numerically to be a close approximation, and 2) how to reduce the number of active streams -- crucial to the overall complexity -- while preserving the sum rate to within a constant loss. The latter results in two practical algorithms: a stream elimination algorithm and a stream ordering algorithm. Finally, we investigate the constant-gap optimality of linearly precoded RS with respect to the capacity. Our result reveals that, while the achievable rate of linear precoding alone can be arbitrarily far from the capacity, the introduction of RS can help achieve the capacity region to within a constant gap in the two-user case. Nevertheless, we prove that the RS scheme's constant-gap optimality does not extend to the three-user case. Specifically, we show, through a pathological example, that the gap between the sum rate and the sum capacity can be unbounded.

Motivated by a simple broadcast channel, we generalize the notions of a less noisy receiver and a more capable receiver to an essentially less noisy receiver and an essentially more capable receiver, respectively. We establish the capacity regions of these classes by borrowing on existing techniques; however, these new classes contain additional interesting classes of broadcast channels, including the BSC/BEC broadcast channel. We also establish the relationships between the new classes and the existing classes.

In this paper, we study the problem of secure communication over the broadcast channel with receiver side information, under the lens of individual secrecy constraints (i.e., information leakage from each message to an eavesdropper is made vanishing). Several coding schemes are proposed by extending known results in broadcast channels to this secrecy setting. In particular, individual secrecy provided via one-time pad signal is utilized in the coding schemes. As a result, we obtain an achievable rate region together with a characterization of the capacity region for special cases of either a weak or strong eavesdropper (compared to both legitimate receivers). Interestingly, the capacity region for the former corresponds to a line and the latter corresponds to a square with missing corners; a phenomenon occurring due to the coupling between user’s rates. At the expense of having a weaker notion of security, positive secure transmission rates are always guaranteed, unlike the case of the joint secrecy constraint.

We derive the capacity region and optimal power allocation scheme for a slowly fading broadcast channel in which minimum rates must be maintained for each user in all fading states, assuming perfect channel state information at the transmitter and at all receivers. We show that the minimum-rate capacity region can be written in terms of the ergodic capacity region of a broadcast channel with an effective noise determined by the minimum rate requirements. This allows us to characterize the optimal power allocation schemes for minimum-rate capacity in terms of the optimal power allocations schemes that maximize ergodic capacity of the broadcast channel with effective noise. Numerical results are provided for different fading broadcast channel models.

This paper shows that the slope at each corner point of the capacity region of the general broadcast channel coincides with that of the randomized time division (hence the Marton) inner bound and the Nair-El Gamal (as well as the Korner-Marton) outer bound. We then show that the optimal superposition coding inner bound by Bandemer, El Gamal, and Kim can be simplified to the convex closure of the union of the Cover-Bergmans UX region and the Cover-van der Meulen UV region. Generalizing a result by Hajek and Pursely on the skewed binary symmetric broadcast channel, we show that for binary input broadcast channels, the UV region reduces to time division further simplifying the superposition coding inner bound. Finally we establish necessary and sufficient conditions for the optimality of the superposition inner bound for skewed binary broadcast channels.

In a broadcast channel, a single transmitter communicates with a number of receivers having different channel capacities available to them. A typical example of such a channel is the over the air TV broadcast. For the two-receiver case, we examine the performance of some common orthogonal transmission methods in terms of their achievable rates. Layered transmission, whereby the information intended for the better channel is superimposed on the portion of information common to both receivers, can provide an optimal solution. On this premise, we construct a bi-rate transmission model for a Gaussian broadcast channel, in which receivers are distributed according to an exponential pdf. A basic grade of service is thus maintained throughout the entire coverage area in addition to a higher quality video offered to the receivers with better reception conditions. The performance evaluation indicates that this model offers a higher per capita data rate comparing to the conventional single rate transmission systems. The multirate paradigm exhibits a stepwise degradation, mitigating the sharp cutoff threshold of the current digital broadcast systems. Application of this multirate broadcast proves very promising in the area of multiresolution transmission of digital HDTV.

A new model for the interference channel with confidential messages (IC-CM) is introduced, where each receiver, besides his noisy observations, is provided with a fixed-length subset, of his choosing, of noiseless observations for the transmitted codewords of both users, making confidential communication more challenging than the previous such model. In addition, in the same spirit, a broadcast channel with confidential messages (BC-CM), where the receivers noiselessly tap into subsets of their choice of the transmitted codeword, is considered. Achievable strong secrecy rate regions for both models are derived. In both models, the size of the subset quantifies a secure rate trade-off between the two receivers. The case of the new BC-CM model with one receiver's noisy observations are degraded with respect to the other receiver, and only the degraded receiver is provided with the subset of noiseless observations, is highlighted. In this case, the receiver with the degraded noisy observations has a positive rate after a certain threshold of his noiseless observations, i.e., with the aid of these symbols.

In this paper, we study a MIMO fading broadcast channel where each receiver has perfect channel state information while the channel state information at the transmitter is acquired by explicit channel feedback from each receiver through capacity-constrained feedback links. Two feedback schemes are considered, i.e., the analog and digital feedback. We analyze the achievable ergodic rates of zero-forcing dirty-paper coding (ZF-DPC), which is a nonlinear precoding scheme inherently superior to linear ZF beamforming. Closed-form lower and upper bounds on the achievable ergodic rates of ZF-DPC with Gaussian inputs and uniform power allocation are derived. Based on the closed-form rate bounds, sufficient and necessary conditions on the feedback channels to ensure nonzero and full downlink multiplexing gain are obtained. Specifically, for analog feedback in both AWGN and Rayleigh fading feedback channels, it is sufficient and necessary to scale the average feedback link SNR linearly with the downlink SNR in order to achieve the full multiplexing gain. While for the random vector quantization-based digital feedback with angle distortion measure in an error-free feedback link, it is sufficient and necessary to scale the number of feedback bits B per user as where M is the number of transmit antennas and is the average downlink SNR.

In this paper, we study duality relations for the fading broadcast channel (BC) under additive white Gaussian noise and a strict ordering of the fading distributions without channel state information at the transmitter and the natural corresponding dual fading multiple-access channel (MAC). We show that if the fading distribution for the weaker user is non-deterministic, the achievable rate region using superposition coding and successive decoding and Gaussian signaling, which is conjectured to be the capacity region, is different from the dual MAC region. Duality holds only in the case of one-sided fading, where the fading distribution for the weaker user is deterministic. Despite this lack of duality, we propose to use the dual MAC in order to approximatively solve a non-convex problem for the BC. Specifically, we consider the problem of weighted sum-rate optimization for the BC and give, under some assumptions, upper bounds on the error incurred using this procedure.

We study the transmission of a common message and three confidential messages over a broadcast channel with two legitimate receivers and an eavesdropper. Each legitimate receiver is interested in decoding two of the three confidential messages, while having the third one as side information. In order to measure the ignorance of the eavesdropper about the confidential messages, we investigate two different secrecy criteria: joint secrecy and individual secrecy. For both criteria, we provide a general achievable rate region. We establish both the joint and individual secrecy capacity if the two legitimate receivers are less noisy than the eavesdropper. We further investigate the scenario where the eavesdropper is less noisy than the two legitimate receivers. It is known that the joint secrecy constraints can not be fulfilled under this scenario, however, we manage to establish a non vanishing capacity region for the individual secrecy case.

Capacity formulas and random-coding and sphere-packing exponents are derived for a generalized family of Gel'fand-Pinsker coding problems. Information is to be reliably transmitted through a noisy channel with random state sequence. Partial information about the state sequence is available to the encoder and decoder. Two families of channels are considered: (1) compound discrete memoryless channels (C-DMC); and (2) channels with arbitrary memory, subject to an additive cost constraint, or more generally to a constraint on the conditional type of the channel output given the input. Both problems are closely connected. For the C-DMC case, our random-coding and sphere-packing exponents coincide at high rates, thereby determining the reliability function of the channel family. The random-coding exponent is achieved using a 3D binning scheme and a maximum penalized mutual information decoder. In the case of arbitrary channels, with memory, a larger random-coding error exponent than in the C-DMC case is obtained. Applications of this study include watermarking, data hiding, communication in presence of partially known interferers, and problems such as broadcast channels, all of which involve the fundamental idea of binning.

In a broadcast channel, a single transmitter communicates to receivers with different channel capacities, a typical example of which is the over-the-air television broadcasting. A natural question that arises is evaluation of the optimal information transfer rate in such an environment. For the two-receiver case, we examine various transmission scenarios in this environment and focus on the theoretically optimal superposition scheme, where the information intended for the better channel is superimposed on the portion of information common to both receivers. As a result, a basic grade of service is maintained throughout the entire coverage area in addition to a higher quality service offered to the receivers with better reception conditions. Using end-to-end distortion and coverage channel signal-to-noise ratio threshold measures, three specific embedded signaling modes are introduced. We demonstrate that a generalized embedding scheme provides a practical trade-off between distortion and coverage radius. The scheme is also formulated in terms of an optimization problem, seeking the best embedding factor for a given application. To verify the theoretical results, we idealize a dual rate transmission system over a Gaussian broadcast channel, in which receivers are distributed according to a circularly symmetric exponential pdf. The numerical results indicate that this model offers a higher per capita data rate comparing to the conventional single rate transmission systems. Application of this multirate broadcast holds promise for multiresolution transmission of digital audio and high definition television.

Achievable rate regions in broadcast channels are usually determined for infinite Gaussian input alphabets. Since these alphabets are not used for practical systems, we investigate the influence of finite signal constellations in the two user AWGN broadcast channel. We show that results derived with Gaussian inputs are not transferable to the finite case. For scenarios where the rate of one user should be maximized whilst a required rate for the other user is delivered we establish design rules.

Preceding with block diagonalization is an attractive approach for approaching sum capacity in multiuser MIMO (multiple input multiple output) broadcast channels. This method though requires either global channel state information at every receiver or an additional training phase, which requires additional system planning. This paper proposes a lattice based multi-user precoder that uses block diagonalization combined with pre-equalization and perturbation for the multiuser MIMO broadcast channel. Achievable rates are computed and used to show that the proposed technique approaches the capacity with block diagonalization and water-filling but does not require the additional channel state information at the receiver. Monte Carlo simulations under the case of equal power allocation show that the proposed method provides better diversity and BER (bit error rate) performance than block diagonalization with a zero-forcing receiver.