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Imperfect Channel State Information at the Transmitter (CSIT) is inevitable in modern wireless communication networks, and results in severe multi-user interference in multi-antenna Broadcast Channel (BC). While the capacity of multi-antenna (Gaussian) BC with perfect CSIT is known and achieved by Dirty Paper Coding (DPC), the capacity and the capacity-achieving strategy of multi-antenna BC with imperfect CSIT remain unknown. Conventional approaches therefore rely on applying communication strategies designed for perfect CSIT to the imperfect CSIT setting. In this work, we break this conventional routine and make two major contributions. First, we show that linearly precoded Rate-Splitting (RS), relying on the split of messages into common and private parts and linear precoding at the transmitter, and successive interference cancellation at the receivers, can achieve larger rate region than DPC in multi-antenna BC with partial CSIT. Second, we propose a novel scheme, denoted as Dirty Paper Coded Rate-Splitting (DPCRS), that relies on RS to split the user messages into common and private parts, and DPC to encode the private parts. We show that the rate region of DPCRS in Multiple-Input Single-Output (MISO) BC with partial CSIT is enlarged beyond that of conventional DPC and that of linearly precoded RS. Gaining benefits from the capability of RS to partially decode the interference and partially treat interference as noise, DPCRS is less sensitive to CSIT inaccuracies, networks loads and user deployments compared with DPC and other existing transmission strategies. [ABSTRACT FROM AUTHOR]

This paper studies the secure transmission in a multiuser broadcast channel where only the statistical channel state information of the eavesdropper is available. We propose to apply secret dirty-paper coding (S-DPC) in this scenario to support the secure transmission of one user and the normal (unclassified) transmission of the other users. By adopting the S-DPC and encoding the secret message in the first place, all the information-bearing signals of the normal transmission are treated as noise by potential eavesdroppers and thus provide secrecy for the secure transmission. In this way, the proposed approach exploits the intrinsic secrecy of multiuser broadcasting and can serve as an energy-efficient alternative to the traditional artificial noise (AN) scheme. To evaluate the secrecy performance of this approach and compare it with the AN scheme, we propose two S-DPC-based secure transmission schemes for maximizing the secrecy rate under constraints on the secrecy outage probability (SOP) and the normal transmission rates. The first scheme directly optimizes the covariance matrices of the transmit signals, and a novel approximation of the intractable SOP constraint is derived to facilitate the optimization. The second scheme combines zero-forcing dirty-paper coding and AN, and the optimization involves only power allocation. We establish efficient numerical algorithms to solve the optimization problems for both schemes. Theoretical and simulation results confirm that, in addition to supporting the normal transmission, the achievable secrecy rates of the proposed schemes can be close to that of the traditional AN scheme, which supports only the secure transmission of one user. [ABSTRACT FROM PUBLISHER]

We consider precoder design for maximizing the weighted sum rate (WSR) of successive zero-forcing dirty paper coding (SZF-DPC). For this problem, the existing precoder designs often assume a sum power constraint (SPC) and rely on the singular value decomposition (SVD). The SVD-based designs are known to be optimal but require high complexity. We first propose a low-complexity optimal precoder design for SZF-DPC under SPC, using the QR decomposition. Then, we propose an efficient numerical algorithm to find the optimal precoders subject to per-antenna power constraints (PAPCs). To this end, the precoder design for PAPCs is formulated as an optimization problem with a rank constraint on the covariance matrices. A well-known approach to solve this problem is to relax the rank constraints and solve the relaxed problem. Interestingly, for SZF-DPC, we are able to prove that the rank relaxation is tight. Consequently, the optimal precoder design for PAPCs is computed by solving the relaxed problem, for which we propose a customized interior-point method that exhibits a superlinear convergence rate. Two suboptimal precoder designs are also presented and compared to the optimal ones. We also show that the proposed numerical method is applicable for finding the optimal precoders for block diagonalization scheme. [ABSTRACT FROM PUBLISHER]

Dirty paper coding (DPC) scheme is the capacity achieving transmission technique in multiuser MIMO downlink channels. As a suboptimal solution to DPC, successive zero-forcing DPC (SZF-DPC) has been proposed recently. The zero-interference constraint in designing the precoding matrices limits the number of supportable users. In this correspondence, we propose three low-complexity suboptimal user scheduling algorithms to exploit the multiuser diversity gain in SZF-DPC as the number of users grows. The first algorithm greedily maximizes the true sum rate. The second algorithm is based on eigenvalues. The third algorithm relies on the diagonal elements of the effective channel matrix since eigenvalues and diagonal entries of a Hermitian matrix have a strong relationship. Simulation results show that the proposed scheduling algorithms can obtain a significant fraction of sum rate of the optimal solution. Furthermore, the performance analysis is provided to prove that the proposed user selection algorithms can achieve the same asymptotic sum rate as that of DPC. [ABSTRACT FROM AUTHOR]

We introduce a fundamental lemma called the Poisson matching lemma, and apply it to prove one-shot achievability results for various settings, namely channels with state information at the encoder, lossy source coding with side information at the decoder, joint source-channel coding, broadcast channels, distributed lossy source coding, multiple access channels and channel resolvability. Our one-shot bounds improve upon the best known one-shot bounds in most of the aforementioned settings (except multiple access channels and channel resolvability, where we recover bounds comparable to the best known bounds), with shorter proofs in some settings even when compared to the conventional asymptotic approach using typicality. The Poisson matching lemma replaces both the packing and covering lemmas, greatly simplifying the error analysis. This paper extends the work of Li and El Gamal on Poisson functional representation, which mainly considered variable-length source coding settings, whereas this paper studies fixed-length settings, and is not limited to source coding, showing that the Poisson functional representation is a viable alternative to typicality for most problems in network information theory. [ABSTRACT FROM AUTHOR]

A memoryless bivariate Gaussian source is transmitted to a pair of receivers over an average-power limited bandwidth-matched Gaussian broadcast channel. Based on their observations, Receiver 1 reconstructs the first source component while Receiver 2 reconstructs the second source component both seeking to minimize the expected squared-error distortions. In addition to the source transmission digital information at a specified rate should be conveyed reliably to Receiver 1–the “stronger” receiver. Given the message rate we characterize the achievable distortions region. Specifically, there is an ${\sf SNR}$ -threshold below which Dirty Paper coding of the digital information against a linear combination of the source components is optimal. The threshold is a function of the digital information rate, the source correlation and the distortion at the “stronger” receiver. Above this threshold a Dirty Paper coding extension of the Tian-Diggavi-Shamai hybrid scheme is shown to be optimal. [ABSTRACT FROM AUTHOR]

In this correspondence, we compare the achievable throughput for the optimal strategy of dirty paper coding (DPC) to that achieved with suboptimal and lower complexity linear precoding techniques (zero-forcing and block diagonalization). Both strategies utilize all available spatial dimensions and therefore have the same multiplexing gain, but an absolute difference in terms of throughput does exist. The sum rate difference between the two strategies is analytically computed at asymptotically high SNR. Furthermore, the difference is not affected by asymmetric channel behavior when each user has a different average SNR. Weighted sum rate maximization is also considered. In the process, it is shown that allocating user powers in direct proportion to user weights asymptotically maximizes weighted sum rate. [ABSTRACT FROM AUTHOR]

This paper derives the maximum achievable sum-rate and presents the optimal encoding/decoding framework for rate-diverse wireless network coding (RD-WNC) over broadband channels consisting of multiple parallel subchannels. RD-WNC applies to a communication scenario in which a base station wants to deliver two different messages with different rates to two users. The base station combines the two separate messages into one network-coded message and broadcasts the network-coded message to both users. Each user then extracts its desired message from the network-coded message by subtracting from it the other message, which we assume to be side information available to the user. Deriving the maximum achievable sum-rate for RD-WNC is challenging when the channel consists of multiple parallel subchannels with different channel coefficients (e.g., the subcarrier channels of OFDM systems), since apart from the rate allocation between the two users, optimal power allocation among multiple subchannels needs to be identified. The first contribution of this paper is a new “mountain-leveling” power allocation algorithm to achieve the maximum sum-rate. With the resulting power allocation, we can then achieve the corresponding optimal sum-rate by having a separate encoding/decoding mechanism for each subchannels, but doing so is cumbersome and complex when the number of subchannels is large. The second contribution of this paper is a practical encoding/decoding framework using only one encoder-decoder mechanism for all subchannels without sacrificing sum-rate optimality. We provide numerical results to corroborate our theoretical findings and to demonstrate the benefits of our encoding/decoding framework. [ABSTRACT FROM AUTHOR]

In wireless networks, the link connectivity may be intermittent due to shadowing, burstiness of data arrival, or uncoordinated resource allocation. In this paper, we model the intermittence of links as Bernoulli distributed random channel states, termed intermittence channel states, and study the impact of the corresponding channel state information at the transmitter (CSIT) in a two-user Gaussian broadcast channel (BC). Moreover, due to the heterogeneous timeliness of intermittence channel states, the CSIT considered in this paper is hybrid. More specifically, the CSIT of each link can be perfectly (causally or non-causally) available, delayed, or not available. When the links are connected, we adopt a general setting that the received signal-to-noise ratios can be different. Our contribution is the characterization of the capacity regions of intermittent Gaussian BC to within bounded gaps for all combinations of hybrid CSIT, except for scenario DN (delayed CSIT of receiver 1, no CSIT of receiver 2). For scenario DN, we propose an opportunistic physical layer network coding scheme that achieves a strictly larger degree-of-freedom (DoF) region than the no-CSIT DoF region. As a corollary, single-user CSIT is able to increase the sum DoF for intermittent Gaussian BC (also the capacity region for the erasure BC, as a by-product). This result is in sharp contrast to the recent negative result by Davoodi and Jafar, where it is shown that for fast-fading multiple-input single-output BC with continuous channel states, single-user CSIT does not help at all in terms of sum DoF. [ABSTRACT FROM AUTHOR]

In wireless communication systems, channel state feedback (CSF) is widely used to improve link performance. However, CSF consumes extra system resources and results in transmission overhead. In this paper, we evaluate such resource consumption in terms of bit rate and provide an explicit expression for the lower bound of the CSF overhead. We propose an overhead optimization mechanism under the constraint of channel state reconstruction accuracy. The numerical simulations show that our paper is beneficial to select the optimum CSF parameters, including the average bit number and channel state feedback period. It is also shown that the proposed overhead optimization scheme is able to reduce the system resource consumption with a guaranteed reconstruction accuracy. [ABSTRACT FROM AUTHOR]

In this paper, a new two-phase-feedback-based user-scheduling-and-beamforming method is proposed for multi-user multiple-input multiple-output downlink in the context of two-stage beamforming. The key ideas of the proposed method are: 1) to use a set of orthogonal reference beams and construct a cone around each reference beam to select “nearly-optimal” semi-orthogonal users based only on channel quality indicator feedback; and 2) to apply post-user-selection beam design with zero-forcing beamforming (ZFBF) based on channel state information (CSI) feedback only from the selected users. It is proven that the proposed scheduling-and-beamforming method is asymptotically optimal as the number of users increase. Furthermore, the proposed scheduling-and-beamforming method almost achieves the performance of the existing semi-orthogonal user selection with ZFBF that requires full CSI for all users, with a significantly reduced amount of required channel information which is even less than that required by random beamforming. [ABSTRACT FROM PUBLISHER]

Uplink-downlink duality refers to the fact that under a sum-power constraint, the capacity regions of a Gaussian multiple-access channel and a Gaussian broadcast channel with Hermitian transposed channel matrices are identical. This paper generalizes this result to a cooperative cellular network, in which remote access-points are deployed as relays in serving the users under the coordination of a central processor (CP). In this model, the users and the relays are connected over noisy wireless links, while the relays and the CP are connected over noiseless but rate-limited fronthaul links. Based on a Lagrangian technique, this paper establishes a duality relationship between such a multiple-access relay channel and broadcast relay channel, under the assumption that the relays use compression-based strategies. Specifically, we show that under the same total transmit power constraint and individual fronthaul rate constraints, the achievable rate regions of the Gaussian multiple-access and broadcast relay channels are identical, when either independent compression or Wyner-Ziv and multivariate compression strategies are used. The key observations are that if the beamforming vectors at the relays are fixed, the sum-power minimization problems under the achievable rate and fronthaul constraints in both the uplink and the downlink can be transformed into either a linear programming or a semidefinite programming problem depending on the compression technique, and that the uplink and downlink problems are Lagrangian duals of each other. Moreover, the dual variables corresponding to the downlink rate constraints become the uplink powers; the dual variables corresponding to the downlink fronthaul constraints become the uplink quantization noises. This duality relationship enables an efficient algorithm for optimizing the downlink transmission and relaying strategies based on the uplink. [ABSTRACT FROM AUTHOR]

This paper derives upper and lower bounds on the secrecy capacity-memory tradeoff of a wiretap erasure broadcast channel (BC) with ${\mathsf{K}}_{w} $ weak receivers and ${\mathsf {K}}_{s} $ strong receivers, where weak receivers and strong receivers have the same erasure probabilities and cache sizes, respectively. The lower bounds are achieved by the schemes that meticulously combine joint cache-channel coding with wiretap coding and key-aided one-time pads. The presented upper bound holds more generally for arbitrary degraded BCs and arbitrary cache sizes. When only weak receivers have cache memories, upper and lower bounds coincide for small and large cache memories, thus providing the exact secrecy capacity-memory tradeoff for this setup. The derived bounds further allow us to conclude that the secrecy capacity is positive even when the eavesdropper is stronger than all the legitimate receivers with cache memories. Moreover, they show that the secrecy capacity-memory tradeoff can be significantly smaller than its non-secure counterpart, but it grows much faster when cache memories are small. This paper also presents a lower bound on the global secrecy capacity-memory tradeoff where one is allowed to optimize the cache assignment subject to a total cache budget. It is close to the best known lower bound without secrecy constraint. For small total cache budget, the global secrecy capacity-memory tradeoff is achieved by assigning all the available cache memory uniformly over all the receivers if the eavesdropper is stronger than all the legitimate receivers, and it is achieved by assigning the cache memory uniformly only over the weak receivers if the eavesdropper is weaker than the strong receivers. [ABSTRACT FROM AUTHOR]

In this paper, we propose an interference alignment (IA) scheme for the multiple-input multiple-output (MIMO) uplink cellular network with the help of a relay which operates in half-duplex mode. The proposed scheme only requires global channel state information (CSI) knowledge at the relay, with no transmitter beamforming and time extension at the user equipment (UE), which differs from conventional IA schemes for cellular networks. We derive the feasibility condition of the proposed scheme for the general cellular network configuration and analyze the degrees-of-freedom (DoF) performance of the proposed IA scheme while providing a closed-form beamformer design at the relay. Extensions of the proposed scheme to downlink and full-duplex cellular networks are also proposed in this paper. The DoF performance of the proposed scheme is compared to those of linear IA scheme and relay-aided interference management scheme for a cellular network with no time extension. It is also shown that advantages similar to those in the uplink case can be obtained for the downlink case through the duality of a relay-aided interfering multiple-access channel (IMAC) and an interfering broadcast channel (IBC). Furthermore, the proposed scheme for a full-duplex cellular network is shown to have advantages identical to those of a number of proposed half-duplex cellular cases. [ABSTRACT FROM AUTHOR]

Linear coding schemes have been the main choice of coding for the additive white Gaussian noise broadcast channel (AWGN-BC) with noiseless feedback in the literature. The achievable rate regions of these schemes go well beyond the capacity region of the AWGN-BC without feedback. In this paper, a concatenated coding design for the $K$-user AWGN-BC with noisy feedback is proposed that relies on linear schemes as inner codes to achieve rate tuples outside the no-feedback capacity region. The boundary of an achievable rate region of purely linear coding schemes for noiseless feedback is shown to be arbitrarily closely approached by the concatenated coding scheme for sufficiently small feedback noise levels. Then, a linear coding scheme for the $K$-user symmetric AWGN-BC with noisy feedback is presented and optimized for use in the concatenated coding scheme. For noiseless feedback, the presented linear coding scheme achieves the optimal sum-rate of linear-feedback coding. An upper bound on the inner code blocklength needed to achieve a sum-rate above no-feedback sum-capacity is derived. [ABSTRACT FROM PUBLISHER]

This paper studies a multiple-input–single-output (MISO) broadcast channel (BC) featuring simultaneous wireless information and power transfer, where a multiantenna access point (AP) delivers both information and energy via radio signals to multiple single-antenna receivers simultaneously, and each receiver implements either information decoding (ID) or energy harvesting (EH). In particular, pseudorandom sequences that are a priori known and therefore can be cancelled at each ID receiver are used as the energy signals, and the information-theoretically optimal dirty paper coding is employed for the information transmission. We characterize the capacity region for ID receivers by solving a sequence of weighted sum-rate (WSR) maximization (WSRMax) problems subject to a maximum sum-power constraint for the AP, and a set of minimum harvested power constraints for individual EH receivers. The problem corresponds to a new form of WSRMax problem in MISO-BC with combined maximum and minimum linear transmit covariance constraints (MaxLTCCs and MinLTCCs), which differs from the celebrated capacity region characterization problem for MISO-BC under a set of MaxLTCCs only and is challenging to solve. By extending the general BC–multiple-access-channel duality, which is only applicable to WSRMax problems with MaxLTCCs, and applying the ellipsoid method, we propose an efficient iterative algorithm to solve this problem globally optimally. Furthermore, we also propose two suboptimal algorithms with lower complexity by assuming that the information and energy signals are designed separately. Finally, numerical results are provided to validate our proposed algorithms. [ABSTRACT FROM PUBLISHER]

This paper studies lossy transmission of a memoryless bivariate Gaussian source over a bandwidth-mismatched memoryless Gaussian broadcast channel with two receivers, where each receiver is interested in reconstructing only one source component. For both bandwidth expansion and compression regimes, novel hybrid digital/analog (HDA) coding schemes are proposed. With appropriate choice of parameters, our schemes are shown to specialize to separate source–channel coding studied by Gao and Tuncel, and is, therefore, superior to it in both bandwidth regimes. Our scheme for bandwidth expansion also outperforms the HDA coding scheme of Behroozi et al. On the other hand, if a proposed conjecture (supported by numerical observations) is indeed true, the same superiority follows for the bandwidth compression regime as well. Finally, when the bandwidth expansion/compression ratio approaches 1, both of our schemes become optimal as their performance approaches that of the bandwidth-matched scheme of Tian et al. [ABSTRACT FROM PUBLISHER]

This paper aims to characterize the capacity limits of a wireless cellular network with a full-duplex (FD) base-station (BS) and half-duplex user terminals, in which three independent messages are communicated: the uplink message m1 from the uplink user to the BS, the downlink message m2 from the BS to the downlink user, and the device-to-device (D2D) message m3 from the uplink user to the downlink user. From an information theoretical perspective, the overall network can be viewed as a generalization of the FD relay broadcast channel with a side message transmitted from the relay to the destination. We begin with a simpler case that involves the uplink and downlink transmissions of (m1, m2) only, and propose an achievable rate region based on a novel strategy that uses the BS as a FD relay to facilitate the interference cancellation at the downlink user. We also prove a new converse, which is strictly tighter than the cut-set bound, and characterize the capacity region of the scalar Gaussian FD network without a D2D message to within a constant gap. This paper further studies a general setup wherein (m1, m2, m3) are communicated simultaneously. To account for the D2D message, we incorporate Marton’s broadcast coding into the previous scheme to obtain a larger achievable rate region than the existing ones in the literature. We also improve the cut-set bound by means of genie and show that by using one of the two simple rate-splitting schemes, the capacity region of the scalar Gaussian FD network with a D2D message can already be reached to within a constant gap. Finally, a generalization to the vector Gaussian channel case is discussed. Simulation results demonstrate the advantage of using the BS as relay in enhancing the throughput of the FD cellular network. [ABSTRACT FROM AUTHOR]

In this paper, we consider a status updating system where updates are generated at a constant rate at $K$ sources and sent to the corresponding recipients through a noise-free broadcast channel. We assume that perfect channel state information (CSI) is available at the transmitter before each transmission, and the transmitter is able to utilize the CSI to precode the updates. Our object is to design optimal precoding schemes to minimize the summed average age of information (AoI) at the recipients. Under various assumptions on the size of each update $B$ , the number of transmit antennas $M$ , and the number of receive antennas $N$ at each user, this paper identifies the corresponding age-optimal precoding and transmission scheduling strategies. Specifically, for the case when $N=1$ , a round-robin based updating scheme is shown to be optimal. For the two-user systems with $N>B$ or $M\notin [N:2N]$ , framed updating schemes are proven to be optimal. For other cases in the two-user systems, a framed alternating updating scheme is proven to be 2-optimal. [ABSTRACT FROM AUTHOR]

Caching is an efficient way to reduce network traffic congestion during peak hours, by storing some content at the user’s local cache memory, even without knowledge of user’s later demands. Maddah-Ali and Niesen proposed a two-phase (placement phase and delivery phase) coded caching strategy for broadcast channels with cache-aided users. This paper investigates the same model under the constraint that content is placed uncoded within the caches, that is, when bits of the files are simply copied within the caches. When the cache contents are uncoded and the users’ demands are revealed, the caching problem can be connected to an index coding problem. This paper focuses on deriving fundamental performance limits for the caching problem by using tools for the index coding problem that were either known or are newly developed in this work. First, a converse bound for the caching problem under the constraint of uncoded cache placement is proposed based on the “acyclic index coding converse bound.” This converse bound is proved to be achievable by the Maddah-Ali and Niesen’s scheme when the number of files is not less than the number of users, and by a newly derived index coding achievable scheme otherwise. The proposed index coding achievable scheme is based on distributed source coding and strictly improves on the widely used “composite (index) coding” achievable bound and its improvements, and is of independent interest. An important consequence of the findings of this paper is that advancements on the coded caching problem posed by Maddah-Ali and Niesen are thus only possible by considering strategies with coded placement phase. A recent work by Yu et al has however shown that coded cache placement can at most half the network load compared to the results presented in this paper. [ABSTRACT FROM AUTHOR]

This paper considers a state dependent broadcast channel with one transmitter, Alice, and two receivers, Bob and Eve. The problem is to effectively convey (“amplify”) the channel state sequence to Bob while “masking” it from Eve. The extent to which the state sequence cannot be masked from Eve is referred to as leakage. This can be viewed as a secrecy problem, where we desire that the channel state itself be minimally leaked to Eve while being communicated to Bob. This paper is aimed at characterizing the tradeoff region between amplification and leakage rates for such a system. An achievable coding scheme is presented, wherein the transmitter transmits a partial state information over the channel to facilitate the amplification process. For the case when Bob observes a stronger signal than Eve, the achievable coding scheme is enhanced with secure refinement. Outer bounds on the tradeoff region are also derived, and used in characterizing some special case results. In particular, the optimal amplification-leakage rate difference, called as differential amplification capacity, is characterized for the reversely degraded discrete memoryless channel, the degraded binary, and the degraded Gaussian channels. In addition, for the degraded Gaussian model, the extremal corner points of the tradeoff region are characterized, and the gap between the outer bound and achievable rate-regions is shown to be less than half a bit for a wide set of channel parameters. [ABSTRACT FROM PUBLISHER]

This paper introduces Manhattan sampling in two and higher dimensions, and proves sampling theorems for them. In 2-D, Manhattan sampling, which takes samples densely along a Manhattan grid of lines, can be viewed as sampling on the union of two rectangular lattices, one dense horizontally and the other vertically, with the coarse spacing of each being a multiple of the fine spacing of the other. The sampling theorem shows that the images bandlimited to the union of the Nyquist regions of the two rectangular lattices can be recovered from their Manhattan samples, and an efficient procedure for doing so is given. Such recovery is possible even though there is an overlap among the spectral replicas induced by Manhattan sampling. In three and higher dimensions, there are many possible configurations for Manhattan sampling, each consisting of the union of special rectangular lattices called bi-step lattices. This paper identifies them, proves a sampling theorem showing that the images bandlimited to the union of the Nyquist regions of the bi-step rectangular lattices are recoverable from Manhattan samples, presents an efficient onion-peeling procedure for doing so, and shows that the union of Nyquist regions is as large as any bandlimited region, such that all images supported by such can be stably reconstructed from samples taken at the rate of the Manhattan sampling. It also develops a special representation for the bi-step lattices with a number of useful properties. While most of this paper deals with continuous-space images, Manhattan sampling of discrete-space images is also considered, for infinite, as well as finite, support images. [ABSTRACT FROM AUTHOR]

In this paper, we study a security problem on a simple wiretap network, consisting of a source node S, a destination node D, and an intermediate node R. The intermediate node connects the source and the destination nodes via a set of noiseless parallel channels, with sizes n1 and n2 , respectively. A message $M$ is to be sent from S to D. The information in the network may be eavesdropped by a set of wiretappers. The wiretappers cannot communicate with one another. Each wiretapper can access a subset of channels, called a wiretap set. All the chosen wiretap sets form a wiretap pattern. A random key $K$ is generated at S, and a coding scheme on $(M, K)$ is employed to protect $M$ . We define two decoding classes at D. In Class-I, only $M$ is required to be recovered, and in Class-II, both $M$ and $K$ are required to be recovered. The objective is to minimize $H(K)/H(M)$ for a given wiretap pattern under the perfect secrecy constraint. The first question we address is whether routing is optimal on this simple network. By enumerating all the wiretap patterns on the Class-I/II (3, 3) networks and harnessing the power of Shannon-type inequalities, we find that gaps exist between the bounds implied by routing and the bounds implied by Shannon-type inequalities for a small fraction (<2%) of all the wiretap patterns. The second question we investigate is the following: What is $\min H(K)/H(M)$ for the remaining wiretap patterns where gaps exist? We study some simple wiretap patterns and find that their Shannon bounds (i.e., the lower bound induced by Shannon-type inequalities) can be achieved by linear codes, which means routing is not sufficient even for the (3, 3) network. For some complicated wiretap patterns, we study the structures of linear coding schemes under the assumption that they can achieve the corresponding Shannon bounds. This paper indicates that the determination of the entropic region of six linear vector spaces cannot be sidestepped. Some subtle issues on the network models are discussed, and interesting observations are stated. [ABSTRACT FROM AUTHOR]

Consider a Gaussian multiple-input multiple-output (MIMO) multiple-access channel (MAC) with channel matrix \mathbf H and a Gaussian MIMO broadcast channel (BC) with channel matrix \mathbf H ^\mathsf T . For the MIMO MAC, the integer-forcing architecture consists of first decoding integer-linear combinations of the transmitted codewords, which are then solved for the original messages. For the MIMO BC, the integer-forcing architecture consists of pre-inverting the integer-linear combinations at the transmitter, so that each receiver can obtain its desired codeword by decoding an integer-linear combination. In both the cases, integer-forcing offers higher achievable rates than zero-forcing while maintaining a similar implementation complexity. This paper establishes an uplink-downlink duality relationship for integer-forcing, i.e., any sum rate that is achievable via integer-forcing on the MIMO MAC can be achieved via integer-forcing on the MIMO BC with the same sum power and vice versa. Using this duality relationship, it is shown that integer-forcing can operate within a constant gap of the MIMO BC sum capacity. Finally, the paper proposes a duality-based iterative algorithm for the non-convex problem of selecting optimal beamforming and equalization vectors, and establishes that it converges to a local optimum. [ABSTRACT FROM PUBLISHER]

This paper addresses lossy transmission of a common source over a broadcast channel when there is correlated side information at the receivers, with emphasis on the quadratic Gaussian and binary Hamming cases. A digital scheme that combines ideas from the lossless version of the problem, i.e., Slepian-Wolf coding over broadcast channels, and dirty paper coding, is presented and analyzed. This scheme uses layered coding where the common layer information is intended for both receivers and the refinement information is destined only for one receiver. For the quadratic Gaussian case, a quantity characterizing the combined quality of each receiver is identified in terms of channel and side information parameters. It is shown that it is more advantageous to send the refinement information to the receiver with "better" combined quality. In the case where all receivers have the same overall quality, the presented scheme becomes optimal. Unlike its lossless counterpart, however, the problem eludes a complete characterization. [ABSTRACT FROM AUTHOR]

In this paper, we investigate joint retrospective interference alignment (RIA) and caching schemes for multiple-input single-output (MISO) broadcast channels (BC) with delayed channel state information at the transmitter (CSIT). By exploiting the cached content, we propose one sophisticated cache-aided RIA scheme to cancel the interference. Importantly, our scheme takes the number of symbols in a packet into account, as different number of symbols in a packet result in different system configuration, which may have significant impact on the design of the transmission scheme and achievable degrees of freedom (DoF). Furthermore, we present two theorems to quantify the achievable sum DoF of the proposed cached-aided RIA scheme for different system configuration. Moreover, the system configuration of the existing cache-aided RIA scheme with mixed CSIT can be treated as a special case in our paper. And also our scheme can simultaneously support more users than the existing cache-aided RIA scheme with mixed CSIT to invoke zero forcing (ZF) precoding, which limits the number of users simultaneously supported. [ABSTRACT FROM AUTHOR]

Characterizing the fundamental energy efficiency (EE) performance of multiple-input–multiple-output interfering broadcast channels (MIMO-IFBC) is important for the design of green wireless system. In this paper, we propose a new network architecture proposition based on EE maximization for Multi-Cell MIMO-IFBC within the context of interference alignment (IA). Particularly, EE is maximized subject to maximum power and minimum throughput constraints. We propose two schemes to optimize EE for different signal-to-noise ratio (SNR) regions. For high-SNR operating regions, we employ a grouping-based IA scheme to jointly cancel intra- and inter-cell interferences and thus transform the MIMO-IFBC to a single-cell MIMO scenario. A gradient-based power adaptation scheme is proposed based on water-filling power adaptation and singular value decomposition to maximize EE for each cell. For moderate SNR cases, we propose an approach using dirty paper coding (DPC) with the principle of multiple access channel and broadcast channel duality to perform IA while maximizing EE in each cell. The algorithm in its dual form is solved using a subgradient method and a bisection searching scheme. Simulation results demonstrate the superior performance of the proposed schemes over several existing approaches. It also shows that interference-nulling-based IA approaches outperform hybrid DPC-IA approach in high-SNR region, and the opposite occurs in low-SNR region. [ABSTRACT FROM PUBLISHER]

Studies of the MISO Broadcast Channel (BC) with delayed Channel State Information at the Transmitter (CSIT) have so far focused on the sum-rate and Degrees-of-Freedom (DoF) region analysis. In this paper, we investigate for the first time, the error rate performance at finite SNR and the diversity-multiplexing tradeoff (DMT) at infinite SNR of a space-time encoded transmission over a two-user MISO BC with delayed CSIT. We consider the so-called MAT protocol obtained by Maddah-Ali and Tse, which was shown to provide 33% DoF enhancement over TDMA. While the asymptotic DMT analysis shows that MAT is always preferable to TDMA, the Pairwise Error Probability analysis at finite SNR shows that MAT is in fact not always a better alternative to TDMA. Benefits can be obtained over TDMA only at a very high rate or once concatenated with a full-rate full-diversity space-time code. The analysis is also extended to spatially correlated channels, and the influence of transmit correlation matrices and user pairing strategies on the performance are discussed. Relying on statistical CSIT, signal constellations are further optimized to improve the error rate performance of MAT and make it insensitive to user orthogonality. Finally, other transmission strategies relying on delayed CSIT are discussed. [ABSTRACT FROM PUBLISHER]

In coding schemes for the wire-tap channel or for broadcast channels with confidential messages, it is well-known that the sender needs to use stochastic encoding to avoid information about the transmitted confidential message from being leaked to an eavesdropper. In this paper, we investigate the tradeoff between the rate of random numbers needed to realize the stochastic encoding and the rates of common, private, and confidential messages. For the direct theorem, we use the superposition coding scheme for the wire-tap channel, recently proposed by Chia and El Gamal, and its strong security is proved. The matching converse theorem is also established. Our result clarifies that a combination of ordinary stochastic encoding and channel prefixing by channel simulation is suboptimal. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the ergodic downlink sum-rate performance of a system consisting of a set of heterogeneous users. We study three user selection schemes to group near-orthogonal users for simultaneous transmission. The first scheme is a random selection policy that achieves fairness, but does not exploit multi-user diversity. The second scheme is a greedy selection policy that fully exploits multi-user diversity, but does not achieve fairness, and the third scheme achieves fairness while partially exploiting multi-user diversity. We also consider two beamforming methods for data transmission, namely, maximum-ratio transmission and zero-forcing beamforming. In all scheduling schemes studied in the paper, there is a key parameter that controls the degrees of orthogonality of channel directions between co-scheduled users. We focus on optimally setting this parameter for each scheduling scheme such that the ergodic downlink sum-rate is maximized. To this end, we derive analytical expressions for the ergodic downlink sum-rate considering each scheduling scheme. Numerical results are also presented to provide further insights. [ABSTRACT FROM PUBLISHER]

To address the exponentially rising demand for wireless content, the use of caching is emerging as a potential solution. It has been recently established that joint design of content delivery and storage (coded caching) can significantly improve performance over conventional caching. Coded caching is well suited to emerging heterogeneous wireless architectures which consist of a dense deployment of local-coverage wireless access points (APs) with high data rates, along with sparsely-distributed, large-coverage macro-cell base stations (BS). This enables design of coded caching-and-delivery schemes that equip APs with storage, and place content in them in a way that creates coded-multicast opportunities for combining with macro-cell broadcast to satisfy users even with different demands. Such coded-caching schemes have been shown to be order-optimal with respect to the BS transmission rate, for a system with single-level content, i.e., one where all content is uniformly popular. In this paper, we consider a system with non-uniform popularity content which is divided into multiple levels, based on varying degrees of popularity. The main contribution of this paper is the derivation of an order-optimal scheme which judiciously shares cache memory among files with different popularities. To show order-optimality we derive new information-theoretic lower bounds, which use a sliding-window entropy inequality, effectively creating a non-cut-set bound. We also extend the ideas to when users can access multiple caches along with the broadcast. Finally, we consider two extreme cases of user distribution across caches for the multi-level popularity model: a single user per cache (single-user setup) versus a large number of users per cache (multi-user setup), and demonstrate a dichotomy in the order-optimal strategies for these two extreme cases. [ABSTRACT FROM PUBLISHER]

Intelligent reflecting surface (IRS) is a new promising technology that is able to reconfigure the wireless propagation channel via smart and passive signal reflection. In this paper, we investigate the capacity region of a two-user communication network with one access point (AP) aided by $M$ IRS elements for enhancing the user-AP channels, where the IRS incurs negligible delay, thus the user-AP channels via the IRS follow the classic discrete memoryless channel model. In particular, we consider two practical IRS deployment strategies that lead to different effective channels between the users and AP, namely, the distributed deployment where the $M$ elements form two IRSs, each deployed in the vicinity of one user, versus the centralized deployment where all the $M$ elements are deployed in the vicinity of the AP. First, we consider the uplink multiple-access channel (MAC) and derive the capacity/achievable rate regions for both deployment strategies under different multiple access schemes. It is shown that the centralized deployment generally outperforms the distributed deployment under symmetric channel setups in terms of achievable user rates. Next, we extend the results to the downlink broadcast channel (BC) by leveraging the celebrated uplink-downlink (or MAC-BC) duality framework, and show that the superior rate performance of centralized over distributed deployment also holds. Numerical results are presented that validate our analysis, and reveal new and useful insights for optimal IRS deployment in wireless networks. [ABSTRACT FROM AUTHOR]

This paper contains two main contributions concerning the expurgation of hierarchical ensembles for the asymmetric broadcast channel. The first is an analysis of the optimal maximum likelihood (ML) decoders for the weak and strong user. Two different methods of code expurgation will be used, that will provide two competing error exponents. The second is the derivation of expurgated exponents under the generalized stochastic likelihood decoder (GLD). We prove that the expurgated exponents achieved for the hierarchical ensemble under GLD decoding are at least as good as the maximum between the random coding error exponents derived in an earlier work by Averbuch and Merhav (2018) and one of our ML–based expurgated exponents. [ABSTRACT FROM AUTHOR]

In this paper, we design energy-efficient space constellations for multiuser multi-input single-output visible light communication broadcast systems with channel state information (CSI) at the receiver in the three scenarios: 1) with CSI at the transmitter (CSIT); 2) with statistical CSIT; and 3) without CSIT. By utilizing the cooperation of multiuser interference, optimal multidimensional additively uniquely decomposable constellation groups are designed to optimize the received worst case performance metrics of all users subject to two commonly used power constraints, i.e., average and peak optical power constraints. The resulting optimal designs are proved to be pulse amplitude modulated with an optimal beamformer, which can be efficiently attained by numerical search for Scenarios 1 and 2 and be given in a closed form for Scenario 3. One of the common significant advantages of these designs is the fast demodulation of the sum signal from a noisy received signal, since these optimal designs result in an equivalent ideal scalar AWGN channel. Comprehensive computer simulations demonstrate that our designs significantly outperform traditional zero-forcing, minimum mean square error, and time-division methods. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of plausible deniability in an information theoretic framework. We consider a scenario where an entity that eavesdrops through a broadcast channel summons one of the parties in a communication protocol to reveal their message (or signal vector). It is desirable that the summoned party has enough freedom to produce a fake output that is likely plausible given the eavesdropper’s observation. We examine three variants of this problem—message deniability, transmitter deniability, and receiver deniability. In the first setting, the message sender is summoned to produce the sent message. Similarly, in the second and third settings, the transmitter and the receiver are required to produce the transmitted codeword and the received vector, respectively. For each of these settings, we examine the maximum communication rate that allows a given minimum rate of plausible fake outputs. First, for the message deniability problem, we fully characterize the capacity region for general broadcast channels. Next, for the transmitter deniability problem, we give an achievable region for general broadcast channels by fully characterizing the set of rate pairs’ achievable using deterministic coding schemes. Finally, for the receiver deniability problem, we give an achievable rate region for physically degraded broadcast channels. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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We consider an n -relay Gaussian diamond network where a source communicates to a destination with the help of n half-duplex relays. Achieving rates close to the capacity of this network requires to employ all the n relays under an optimal transmit/receive schedule. Even for the moderate values of n different states for the network (since each of the relays can be in either transmitting or receiving mode). In this paper, we investigate whether a significant fraction of the network capacity can be achieved by using transmit/receive schedules that have only few active states and by using only few relays. First, we conjecture that the approximately optimal schedule has at most n+1 states instead of the 2^n possible states. We prove this conjecture for networks of size n\leq 6 by developing a proof strategy and implementing it computationally. Second, we show that routing strategies that only employ the point-to-point communication and two of the relays with a half-duplex schedule that has only two active states can achieve at least half the capacity (approximately) of the network. Techniques from linear programming and submodular functions are used to derive the results. [ABSTRACT FROM AUTHOR]

The index coding problem includes a server, a group of clients, and a set of data chunks. While each client wants a subset of the data chunks and already has another subset as its side information, the server transmits some (uncoded or coded) chunks to the clients over a noiseless broadcast channel. The objective of the problem is to satisfy the demands of all clients with the minimum number of transmissions. This paper investigates the index coding setting from a game-theoretical perspective. We consider selfish clients, where each selfish client has private side information and a private valuation of each data chunk it wants. In this context, our objectives are following: 1) to motivate each selfish client to reveal the correct side information and true valuation of each data chunk it wants; 2) to maximize the social welfare, i.e., the total valuation of the data chunks recovered by the clients minus the total cost incurred by the transmissions from the server. Our main contribution is to jointly develop coding and incentive schemes for achieving the first objective perfectly and achieving the second objective optimally or approximately with guaranteed approximation ratios (potentially within some restricted sets of coding matrices). [ABSTRACT FROM AUTHOR]

This paper asks how much we can gain in terms of bandwidth and user satisfaction, if recommendation systems became bandwidth aware and took into account not only the user preferences, but also the fact that they may need to serve these users under bandwidth constraints, as is the case over wireless networks. We formulate this as a new problem in the context of index coding: we relax the index coding requirements to capture scenarios where each client has preferences associated with messages. The client is satisfied to receive any message she does not already have, with a satisfaction proportional to her preference for that message. We consistently find, over a number of scenarios we sample, that although the optimization problems are in general NP-hard, significant bandwidth savings are possible even when restricted to polynomial time algorithms. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A broadcast strategy for multiple access communication over slowly fading channels is introduced, in which the channel state information is known to only the receiver. In this strategy, the transmitters split their information streams into multiple independent information streams, each adapted to a specific actual channel realization. The major distinction between the proposed strategy and the existing ones is that in the existing approaches, each transmitter adapts its transmission strategy only to the fading process of its direct channel to the receiver, hence, directly adopting a single-user strategy previously designed for the single-user channels. However, the contribution of each user to a network-wide measure (e.g., sum-rate capacity) depends not only on the user’s direct channel to the receiver, but also on the qualities of other channels. Driven by this premise, this paper proposes an alternative broadcast strategy in which the transmitters adapt their transmissions to the combined states resulting from all users’ channels. This leads to generating a larger number of information streams by each transmitter and adopting a different decoding strategy by the receiver. An achievable rate region and an outer bound that capture the tradeoff among the rates of different information layers are established, and it is shown that the achievable rate region subsumes the existing known capacity regions obtained based on adapting the broadcast approach to the single-user channels. [ABSTRACT FROM AUTHOR]

The problem of secure broadcasting with independent secret keys is studied. The particular scenario is analyzed in which a common message has to be broadcast to two legitimate receivers, while keeping an external eavesdropper ignorant of it. The transmitter shares independent secret keys of sufficiently high rates with both legitimate receivers, which can be used in different ways: they can be used as one-time pads to encrypt the common message, as fictitious messages for wiretap coding, or as a hybrid of these. In this paper, capacity results are established when the broadcast channels involving the three receivers are degraded. If both legitimate channels are degraded versions of the eavesdropper’s channel, it is shown that the one-time pad approach is optimal for several cases, yielding corresponding capacity expressions. Alternatively, the wiretap coding approach is shown to be optimal if the eavesdropper’s channel is degraded with respect to both legitimate channels, establishing capacity in this case as well. If the eavesdropper’s channel is neither the strongest nor the weakest, an intricate scheme that carefully combines both concepts of one-time pad and wiretap coding with fictitious messages turns out to be capacity-achieving. Finally we also obtain some results for the general non-degraded broadcast channel. [ABSTRACT FROM PUBLISHER]

The final coverage and associated performance of a single frequency networks (SFNs) is a joint result of the properties of all transmitters in the SFN. Due to the large number of parameters involved in the process, finding the right configuration is quite complex. The purpose of this paper is to find optimal SFN network configurations for second generation digital terrestrial broadcast system (DVB-T2). Offering more options of system parameters than its predecessor DVB-T, DVB-T2 allows large SFN networks. However, self-interference in SFNs gives rise to restrictions on the maximum intertransmitter distance and the network size. In order to make optimum use of the spectrum, the same frequency can be reused over different geographical areas—beyond the reuse distance to avoid co-channel interference. In this paper, a methodology based on theoretical network models is proposed. A number of network architectures and network reference models are considered here for different reception modes in order to study the effects of key planning factors on the maximum SFN size and minimum reuse distance. The results show that maximum bitrate, network size, and reuse distance are closely related. In addition, it has been found that the guard interval is not the only limiting parameter and that its impact strongly depends on the rest of DVB-T2 mode parameters as well as on the network characteristics (equivalent radiated power, effective height, and intertransmitter distance). Assuming that the carrier to noise ratio requirements are in the vicinity of 20 dB and bitrates over 30 Mb/s, it has been found that the network can be as large as 360 \times 360 km (delivering 39.2 Mb/s) or even 720 \times 720 km (delivering 37.5 Mb/s). The reuse distance will also have a complex dependency on the DVB-T2 mode and especially the network parameters, ranging from below 100 to 300 km. [ABSTRACT FROM PUBLISHER]

In this paper, fast fading Gaussian multiuser channels are considered. If the channel state information (CSI) is perfectly known to the transmitter, capacities have been derived for many cases in which the channels satisfy certain information-theoretic orders such as degradedness, or strong/very strong interference. We study the case when only the statistics of the CSI are known at the transmitter, which is an open problem in general. The main contributions of this paper are the following: First, we derive a sufficient condition to construct equivalent (having the same capacity region as the original channel) degraded Gaussian broadcast channels, which is based on the marginal distributions of the channel gains. To achieve this goal, we leverage three schemes: coupling, maximal coupling, and copulas, in addition to the same marginal property. The underlying idea of all schemes is to obtain an equivalent channel by changing the joint distribution in such a way that it satisfies a certain information-theoretic order while ensuring that the marginal distributions of the channels to different users are not changed. The construction of this equivalent multiuser channel allows us to directly apply existing capacity results. We then further derive the capacity regions of Gaussian interference channels with strong and very strong interferences, and also the secrecy capacity of Gaussian wiretap channels, while in all cases, the transmitters know only the statistics of the channels. Several practical examples such as Rayleigh fading and Nakagami- ${m}$ fading illustrate the applicability of the derived results. [ABSTRACT FROM AUTHOR]

In this paper, we study the arbitrarily varying broadcast channel (AVBC) when the state information is available at the transmitter in a causal manner. We establish the inner and outer bounds on both the random code capacity region and the deterministic code capacity region with degraded message sets. The capacity region is then determined for a class of channels satisfying a condition on the mutual information between the strategy variables and the channel outputs. As an example, we consider the arbitrarily varying binary symmetric broadcast channel. We show the cases where the condition holds and, hence, the capacity region is determined and other cases where there is a gap between the bounds. This gap shows that the minimax theorem does not hold for rate regions. [ABSTRACT FROM AUTHOR]

When the users in a MIMO broadcast channel experience different spatial transmit correlation matrices, a class of gains is produced that is denoted transmit correlation diversity. This idea was conceived for channels in which transmit correlation matrices have mutually exclusive eigenspaces, allowing non-interfering training and transmission. This paper broadens the scope of transmit correlation diversity to the case of partially and fully overlapping eigenspaces and introduces techniques to harvest these generalized gains. For the two-user MIMO broadcast channel, we derive achievable degrees of freedom (DoF) and achievable rate regions with/without channel state information at the receiver (CSIR). When CSIR is available, the proposed achievable DoF region is tight in some configurations of the number of receive antennas and the channel correlation ranks. We then extend the DoF results to the $K$ -user case by analyzing the interference graph that characterizes the overlapping structure of the eigenspaces. Our achievability results employ a combination of product superposition in the common part of the eigenspaces, and pre-beamforming (rate splitting) to create multiple data streams in non-overlapping parts of the eigenspaces. Massive MIMO is a natural example in which spatially correlated link gains are likely to occur. We study the achievable downlink sum rate for a frequency-division duplex massive MIMO system under transmit correlation diversity. [ABSTRACT FROM AUTHOR]

This paper studies the capacity of the two-receiver multiple-input broadcast packet erasure channels (PECs) with channel output feedback, which is in contrast with the single-input setting of the existing works. Motivated by the immense success of linear network coding (LNC) in theory and in practice, this paper first focuses on LNC schemes and characterizes the LNC feedback capacity region of two-receiver multiple-input broadcast PECs. A new linear-space-based approach is proposed, which unifies the problems of finding a capacity outer bound and devising the achievability scheme into a single linear programming problem. In particular, an LP solver is used to exhaustively search for the LNC scheme(s) with the best possible throughput, the result of which is thus guaranteed to attain the LNC feedback capacity. It is then proven by pure algebraic arguments that the LNC capacity region matches a simple capacity region outer bound, which proves that the derived LNC capacity region is indeed the true capacity. A byproduct of the above results is a complete LNC capacity region characterization for two-receiver partially Markovian and partially controllable broadcast PECs. [ABSTRACT FROM AUTHOR]