Two-user Broadcast Channel Research Articles

A Single-Letter Upper Bound on the Mismatch Capacity via Multicast Transmission

We introduce a new analysis technique to derive a single-letter upper bound on the mismatch capacity of a stationary, single-user, memoryless channel with a decoding metric <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>. Our bound is obtained by considering a multicast transmission over a two-user broadcast channel with decoding metrics <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\rho $ </tex-math></inline-formula> at the receivers, referred to as <inline-formula> <tex-math notation="LaTeX">$(q,\rho)$ </tex-math></inline-formula>-surely degraded. This channel has the property that the intersection event of correct <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-decoding of receiver 1 and erroneous <inline-formula> <tex-math notation="LaTeX">$\rho $ </tex-math></inline-formula>-decoding of receiver 2 has zero probability for any fixed-composition codebook of a certain composition <inline-formula> <tex-math notation="LaTeX">$P$ </tex-math></inline-formula>. Our bound holds in the strong converse sense of an exponential decay of the probability of correct decoding at rates above the bound. Further, we refine the proof and present a bound that is tighter than that of any choice of <inline-formula> <tex-math notation="LaTeX">$\rho $ </tex-math></inline-formula>. Several examples that demonstrate the strict improvement of our bound compared to previous results are analyzed. Finally, we detect equivalence classes of isomorphic channel-metric pairs <inline-formula> <tex-math notation="LaTeX">$(W,q)$ </tex-math></inline-formula> that share the same mismatch capacity. We prove that if the class contains a matched pair, then our bound is tight and the mismatch capacity of the entire class is fully characterized and is equal to the LM rate, which is achievable by random coding, and may be strictly lower that the matched capacity.

Performance analysis of congestion-aware secure broadcast channels

Congestion-aware scheduling in case of downlink cellular communication has ignored the distribution of diverse content to different clients with heterogeneous secrecy requirements. Other possible application areas that encounter the preceding issue are secure offloading in mobile-edge computing, and vehicular communication. In this paper, we extend the work in Arvanitaki et al. (SN Comput Sci 1(1):53, 2019) by taking into consideration congestion and random access. Specifically, we study a two-user congestion-aware broadcast channel with heterogeneous traffic and different security requirements. We consider two randomized policies for selecting which packets to transmit, one is congestion-aware by taking into consideration the queue size, whereas the other one is congestion-agnostic. We analyse the throughput and the delay performance under two decoding schemes at the receivers, and provide insights into their relative security performance and into how congestion control at the queue holding confidential information can help decrease the average delay per packet. We show that the congestion-aware policy provides better delay, throughput, and secrecy performance for large arrival packet probabilities at the queue holding the confidential information. The derived results also take account of the self-interference caused at the receiver for whom confidential data is intended due to its full-duplex operation while jamming the communication at the other user. Finally, for two decoding schemes, we formulate our problems in terms of multi-objective optimization, which allows for finding a trade-off between the average packet delay for packets intended for the legitimate user and the throughput for the other user under congestion-aware policy.

Secure Degrees of Freedom of Rank-Deficient BCCM and Rank-Deficient ICCM

The secure degrees of freedom (SDoF) of two-user rank-deficient multiple-input multiple-output (MIMO) broadcast channel with confidential messages (BCCM) and two-user rank- deficient MIMO interference channel with confidential messages (ICCM) are studied respectively in this paper. In the systems, each transmitter has $M$ antennas, and each receiver has $N$ antennas. We consider that each transmitter intends to send secure messages to the corresponding receiver, and another receiver can receive the messages but cannot decode them, which ensures that the messages are confidential. Comparing with previous studies on two-user broadcast channel and interference channel, we explore the case that channel matrices are rank-deficient, and the rank of channel matrices can take arbitrary value, $D \leq \text{min} (M,N)$ . For the two rank-deficient channels, BCCM and ICCM, we divide the problem into several regimes according to the different configurations of the rank of channel matrices and the number of antennas at each node. The outer bound of rank-deficient BCCM is inferred from information theoretic methods and the achievable schemes are given by zero forcing techniques. We derive the outer bound of rank-deficient ICCM by taking the minimum region of the three outer bounds, where the first outer bound is the result of rank-deficient interference channel model without secrecy constraints, the second outer bound is obtained by considering secrecy constraints, and the third outer bound is achieved by transmitters cooperation. Then we present the achievable schemes by combining zero-forcing, real interference alignment, and spatial alignment. Finally, we determine the exact SDoF of the rank-deficient BCCM and the rank-deficient ICCM.

A Cooperative Jamming Technique to Protect a Two-User Broadcast Channel with Confidential Messages and an External Eavesdropper

This work addresses the security of a two-user broadcast channel. The challenge of protecting a broadcast channel is associated with the necessity of securing the system, not only against eavesdropping attacks originating from external nodes, but also to ensure that the inside users do not eavesdrop on each other’s information. To address this issue, the present work proposes a cooperative jamming scheme that provides protection against eavesdropping attacks carried out simultaneously by inside users and external eavesdroppers. To achieve this goal, the developed scheme combines real interference alignment with a blind cooperative jamming technique defined in the literature. An information theoretical analysis shows that positive secure degrees of freedom are achievable using the proposed solution.

Delay Performance of a Two-User Broadcast Channel with Security Constraints

In this paper, we consider the two-user broadcast channel with security constraints. We assume that a source broadcasts packets to two receivers, and that one of them has secrecy constraints, i.e., its packets need to be kept secret from the other receiver. The receiver with secrecy constraint has full-duplex capability, allowing it to transmit a jamming signal to increase its secrecy. We derive the average delay per packet and provide simulations and numerical results, where we compare different performance metrics for the cases when both receivers treat interference as noise, when the legitimate receiver performs successive decoding, and when the eavesdropper performs successive decoding. The results show that successive decoding provides better average packet delay for the legitimate user. Furthermore, we define a new metric that characterizes the reduction on the success probability for the legitimate user that is caused by the secrecy constraint. The results show that secrecy poses a significant amount of packet delay for the legitimate receiver when either receiver performs successive decoding. We also formulate an optimization problem, wherein the throughput of the eavesdropper is maximized under delay and secrecy rate constraints at the legitimate receiver. We provide numerical results for the optimization problem, where we show the trade-off between the transmission power for the jamming and the throughput of the non-legitimate receiver. The results provide insights into how channel ordering and encoding differences can be exploited to improve performance under different interference conditions.

Source Broadcasting and Asymmetric Data Transmission With Bandwidth Expansion

We consider the broadcasting of a scalar memoryless Gaussian source over a two-user Gaussian broadcast channel with bandwidth expansion. In concurrent with the source description, a message that should be decoded reliably just by the “higher quality” user is sent. Conditioned on the message rate, we derive a necessary condition for the achievability of a mean-squared-error distortion pair at the two receivers, which extends the Reznic–Feder–Zamir bound. This necessary condition and a sufficient condition that we derive establish the set of achievable energy-distortion exponents for this setting.

Secure Wireless Communications in Broadcast Channels With Confidential Messages

Delivering confidential messages in wireless network is gaining continuous attraction as a fundamental building block for the Internet of things (IoT). This paper overviews the confidential message transmission techniques in broadcast channel (BC) where a transmitter serves multiple users by delivering confidential messages to their intended users. Each confidential message must be prevented from extracting its information by any unintended users. First, we consider a basic network consisting of two users. In the two-user BC, the secret dirty paper coding (S-DPC) achieves the secrecy capacity region. However, since the DPC requires a high computational complexity for characterizing the capacity region, two sub-optimal transmission techniques with low complexities are explained. Second, we extend our discussion to the network including more than two users. For $K$ -user BC with confidential messages, the optimal transmission scheme and the secrecy capacity region have not yet been derived. Instead of presenting the optimal scheme, we explain two sub-optimal transmission techniques and compare their features and performances. In conclusion, we discuss the open problems in the confidential message transmission for networks with more than two users.

Capacity Characterization of UAV-Enabled Two-User Broadcast Channel

Unmanned aerial vehicles (UAVs) have recently gained growing popularity in wireless communications owing to their many advantages such as swift and cost-effective deployment, line-of-sight (LoS) aerial-to-ground link, and controllable mobility in three-dimensional (3D) space. Although prior works have exploited the UAV’s mobility to enhance the wireless communication performance under different setups, the fundamental capacity limits of UAV-enabled/aided multiuser communication systems have not yet been characterized. To fill this gap, we consider, in this paper, a UAV-enabled two-user broadcast channel (BC), where a UAV flying at a constant altitude is deployed to send independent information to two users at different fixed locations on the ground. We aim to characterize the capacity region of this new type of BC over a given UAV flight duration, by jointly optimizing the UAV’s trajectory and transmit power/rate allocations over time, subject to the UAV’s maximum speed and maximum transmit power constraints. First, to draw essential insights, we consider two special cases with asymptotically large/low UAV flight duration/speed, respectively. For the former case, it is shown that a simple hover-fly-hover (HFH) UAV trajectory with time division multiple access (TDMA)-based orthogonal multiuser transmission is capacity-achieving; while in the latter case, the UAV should hover at a fixed location that is nearer to the user with larger achievable rate and in general superposition coding (SC)-based non-orthogonal transmission with interference cancellation at the receiver of the nearer user is required. Next, we consider the general case with finite UAV speed and flight duration. We show that the optimal UAV trajectory should follow a general HFH structure, i.e., the UAV successively hovers at a pair of optimal initial and final locations above the line segment connecting the two users each with a certain amount of time and flies unidirectionally between them at the maximum speed, and SC is generally needed. Furthermore, when TDMA-based transmission is considered for low-complexity implementation, we show that the optimal UAV trajectory still follows an HFH structure, but the hovering locations can only be those above the two users. Extensive simulation results are provided to verify our analysis, which also reveal useful guidelines to the practical design of UAV trajectory and communication jointly.

Delay Minimal Policies in Energy Harvesting Communication Systems

We characterize delay minimal power scheduling policies in energy harvesting communication systems. We consider a continuous-time system, where the delay experienced by each bit is given by the time spent by the bit in the queue waiting to be transmitted to its receiver. We first consider a single-user channel, where the transmitter has a finite-sized battery to save its harvested energy. Data arrives during the course of communication and are saved in a finite data buffer as well. We find the optimal power policy that minimizes the average delay experienced by the bits subject to energy and data causality constraints. We characterize the optimal solution in terms of Lagrange multipliers, and calculate their values in a recursive manner. We show that, different from the existing literature, the optimum transmission power is not constant between the energy and data arrival events; the transmission power starts high, decreases linearly, and potentially reaches zero between energy and data arrivals. Intuitively, untransmitted bits experience cumulative delay due to the bits to be transmitted ahead of them, and hence the reason for transmission power starting high and decreasing over time. Next, we study a multiuser version of this problem, namely, a two-user broadcast channel, and characterize the optimal transmission policies that minimize the sum delay. For this setting, we consider the case, where the transmitter has an infinite-sized battery, and that all data packets intended for the receivers are available at the beginning of the communication session. We characterize the optimal solution in terms of Lagrange multipliers, and present an iterative solution that calculates their values. Our results show that in the optimal policy, both users may not be served simultaneously all the time; there may be times, where only one of the two users is served alone. We also show that the optimal policy may have gaps in transmission in between energy arrivals, where none of the users is served, echoing the results of the single-user setting.

On the Capacity Region of the Parallel Degraded Broadcast Channel With Three Receivers and Three-Degraded Message Sets

We consider a broadcast channel with three receivers and three-degraded message sets, i.e., the transmitter has a common message intended for all three receivers, a message intended for receivers 2 and 3, and a private message intended only for receiver 3. The messages are transmitted over a family of parallel degraded broadcast channels. In the most general case, the broadcast channel consists of the product of six parallel degraded broadcast channels, each with a different order of degradedness. We first consider an achievable rate region of Nair and El Gamal, by appropriately choosing independent input random variables and auxiliary random variables for each subchannel. We then show that the achievable rate region attains the capacity region for two different classes of such broadcast channels, one consisting of the product of five parallel degraded broadcast channels and another consisting of the product of three parallel degraded broadcast channels. To accomplish this, we make use of an information-theoretic inequality that may be proven using the Csiszar-sum identity. Next, we extend the result to the Gaussian case. We consider the aligned Gaussian MIMO broadcast channel consisting of the product of six parallel degraded Gaussian broadcast channels, where the Gaussian noise vectors for each of the users in each of the subchannels follow a degradedness order, i.e., the noise covariance matrices may be ordered in a positive semi-definite sense. We show that the Nair–El Gamal achievable rate region considered in this paper is maximized by Gaussian inputs. To prove that Gaussian inputs are optimal, we prove an extremal entropy inequality employing a new method recently introduced by Geng and Nair to prove the capacity region of the two-user Gaussian MIMO broadcast channel with common and private messages.

Transmit Precoder Design for Two-User Broadcast Channel with Statistical and Delayed CSIT

Transmit Precoder Design for Two-User Broadcast Channel with Statistical and Delayed CSIT

Secure Communications for the Two-User Broadcast Channel With Random Traffic

In this paper, we study the stability region of the two-user broadcast channel (BC) with bursty data arrivals and security constraints. It is assumed that one of the receivers has a secrecy constraint, i.e., its packets need to be kept secret from the other receiver, which is defined based on signal to interference noise ratio. The receiver with secrecy constraint has full-duplex capability to send a jamming signal for improving its service rate. The stability region of the two-user BC with secrecy constraint is characterized for the general decoding case. Then, assuming two different decoding schemes, the respective stability regions are derived. The full-duplex operation of receiver results in self-interference, and the effect of imperfect self-interference cancelation on the stability region is also investigated. The stability region of the BC with a secrecy constraint, where the receivers do not have full duplex capability can be obtained as a special case of the results derived in this paper. In addition, the paper considers the problem of maximizing the saturated throughput of the queue for which there is no secrecy constraint under minimum service guarantees for the other queue. The results provide new insights on the effect of the secrecy constraint on the stability region of the BC. It is found that the stability region with secrecy constraint is sensitive to the degree of self-interference cancelation.

Stable Throughput Region of the Two-User Broadcast Channel

In this paper, we consider the two-user broadcast channel and we characterize its stable throughput region. We start the analysis by providing the stability region for the general case without any specific considerations on transmission and reception mechanisms. We also provide conditions for the stable throughput region to be convex. Subsequently, we study the case where the transmitter uses superposition coding and we consider two special cases for the receivers. The first one is when both receivers treat interference as noise. The second is when the user with a better channel uses successive decoding and the other receiver treats interference as noise.

Channel Correlation Based Zero-Forcing Beamforming in Two-User MISO Broadcast Channel

In this paper, a novel zero-forcing beamforming (ZFBF) is presented for the two-user multiple input single output broadcast channel. Based on the knowledge of channel correlations at the transmitter side, a nonlinear optimization problem is formulated to determine the beamformers so that the weighted ergodic sum-rate is maximized subject to avoiding multi-user interference and meeting a total power constraint. By factorizing each beamformer, the original complicated problem can be transformed into a simpler one. Numerical results show that the performance gap between the proposed ZFBF and the traditional instantaneous channel state information based ZFBF is within 1.5 bits per transmission.

Optimal Rate-Diverse Wireless Network Coding

This paper proposes an encoding/decoding framework for achieving the optimal channel capacities of the two-user broadcast channel where each user (receiver) has the message targeted for the other user (receiver) as side information. Since the link qualities of the channels from the base station to the two users are different, their respective single-user non-broadcast channel capacities are also different. A goal is to simultaneously achieve/approach the single-user non-broadcast channel capacities of the two users with a single broadcast transmission by applying network coding. This is referred to as the rate-diverse wireless network coding problem. For this problem, this paper presents a capacity-achieving framework based on linear-structured nested lattice codes. The significance of the proposed framework, besides its theoretical optimality, is that it suggests a general design principle for linear rate-diverse wireless network coding going beyond the use of lattice codes. We refer to this design principle as the principle of virtual single-user channels . Guided by this design principle, we propose two implementations of our encoding/decoding framework using practical linear codes amenable to decoding with affordable complexities: the first implementation is based on Low Density Lattice Codes (LDLC) and the second implementation is based on Bit-interleaved Coded Modulation (BICM). These two implementations demonstrate the validity and performance advantage of our framework.

On the Energy-Distortion Tradeoff of Gaussian Broadcast Channels with Feedback

This work studies the relationship between the energy allocated for transmitting a pair of correlated Gaussian sources over a two-user Gaussian broadcast channel with noiseless channel output feedback (GBCF) and the resulting distortion at the receivers. Our goal is to characterize the minimum transmission energy required for broadcasting a pair of source samples, such that each source can be reconstructed at its respective receiver to within a target distortion, when the source-channel bandwidth ratio is not restricted. This minimum transmission energy is defined as the energy-distortion tradeoff (EDT). We derive a lower bound and three upper bounds on the optimal EDT. For the upper bounds, we analyze the EDT of three transmission schemes: two schemes are based on separate source-channel coding and apply encoding over multiple samples of source pairs, and the third scheme is a joint source-channel coding scheme that applies uncoded linear transmission on a single source-sample pair and is obtained by extending the Ozarow–Leung (OL) scheme. Numerical simulations show that the EDT of the OL-based scheme is close to that of the better of the two separation-based schemes, which makes the OL scheme attractive for energy-efficient, low-latency and low-complexity source transmission over GBCFs.

Posterior Matching for Gaussian Broadcast Channels with Feedback

In this paper, the posterior matching scheme proposed by Shayevits and Feder is extended to the Gaussian broadcast channel with feedback, and the error probabilities and achievable rate region are derived for this coding strategy by using the iterated random function theory. A variant of the Ozarow-Leung code for the general two-user broadcast channel with feedback can be realized as a special case of our coding scheme. Furthermore, for the symmetric Gaussian broadcast channel with feedback, our coding scheme achieves the linear-feedback sum-capacity like the LQG code and outperforms the Kramer code.

On SDoF of Multi-Receiver Wiretap Channel With Alternating CSIT

We study the problem of secure transmission over a Gaussian multi-input single-output (MISO) two receiver channel with an external eavesdropper, under the assumption that the state of the channel which is available to each receiver is conveyed either perfectly ( $P$ ) or with delay ( $D$ ) to the transmitter. Denoting by $S_{1}$ , $S_{2}$ , and $S_{3}$ , the channel state information at the transmitter (CSIT) of user 1, user 2, and eavesdropper, respectively, the overall CSIT can then alternate between eight possible states, i.e., $(S_{1},S_{2},S_{3}) \in \{P,D\}^{3}$ . We denote by $\lambda _{S_{1} S_{2} S_{3}}$ the fraction of time during which the state $S_{1}S_{2}S_{3}$ occurs. Under these assumptions, we first consider the Gaussian MISO wiretap channel and characterize the secure degrees of freedom (SDoF). Next, we consider the general multi-receiver setup and characterize the SDoF region of fixed hybrid states $PPD$ , $PDP$ , and $DDP$ . We then focus our attention on the symmetric case in which $\lambda _{PDD}=\lambda _{DPD}$ . For this case, we establish bounds on SDoF region. The analysis reveals that alternating CSIT allows synergistic gains in terms of SDoF, and shows that by opposition to encoding separately over different states, joint encoding across the states strictly enables better secure rates. Furthermore, we specialize our results for the two receivers channel with an external eavesdropper to the two-user broadcast channel. We show that the synergistic gains in terms of SDoF by alternating CSIT are not restricted to multi-receiver wiretap channels, and can also be harnessed under broadcast setting.

Coherent Product Superposition for Downlink Multiuser MIMO

In a two-user broadcast channel where one user has full CSIR and the other has none, a recent result showed that TDMA is strictly suboptimal and a product superposition requiring non-coherent signaling achieves DoF gains under many antenna configurations. This work introduces product superposition in the domain of coherent signaling with pilots, demonstrates the advantages of product superposition in low-SNR as well as high-SNR, and established DoF gains in a wider set of receiver antenna configurations. Two classes of decoders, with and without interference cancellation, are studied. Achievable rates are established by analysis and illustrated by simulations.

Statistical Beamforming on the Grassmann Manifold for the Two-User Broadcast Channel

A Rayleigh fading spatially correlated broadcast setting with <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$M = 2$</tex></formula> antennas at the transmitter and two users (each with a single antenna) is considered. It is assumed that the users have perfect channel information about their links, whereas the transmitter has only statistical information of each user's link (covariance matrix of the vector channel). A low-complexity linear beamforming strategy that allocates equal power and one spatial eigenmode to each user is employed at the transmitter. Beamforming vectors on the Grassmann manifold that depend only on statistical information are to be designed at the transmitter to maximize the ergodic sum-rate delivered to the two users. Toward this goal, the beamforming vectors are first fixed and a closed-form expression is obtained for the ergodic sum-rate in terms of the covariance matrices of the links. This expression is nonconvex in the beamforming vectors ensuring that the classical Lagrange multiplier technique is not applicable. Despite this difficulty, the optimal solution to this problem is shown to be the same as the solution to the maximization of an appropriately defined average signal-to-interference and noise ratio metric for each user. This solution is the dominant generalized eigenvector of a pair of positive-definite matrices where the first matrix is the covariance matrix of the forward link and the second is an appropriately designed “effective” interference covariance matrix. In this sense, our work is a generalization of optimal signalling along the dominant eigenmode of the transmit covariance matrix in the single-user case. Finally, the ergodic sum-rate for the general broadcast setting with <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$M$</tex></formula> antennas at the transmitter and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$M$</tex> </formula> -users (each with a single antenna) is obtained in terms of the covariance matrices of the links and the beamforming vectors.