We consider a broadcast scenario where one transmitter communicates with two receivers under quality-of-service constraints. The transmitter initially employs superposition coding strategies with arbitrarily distributed signals and sends data to both receivers. Regarding the channel state conditions, the receivers perform successive interference cancellation to decode their own data. We express the effective capacity region that provides the maximum allowable sustainable data arrival rate region at the transmitter buffer or buffers. Given an average transmission power limit, we provide a two-step approach to obtain the optimal power allocation policies that maximize the effective capacity region. Then, we characterize the optimal decoding regions at the receivers in the space spanned by the channel fading power values. We finally substantiate our results with numerical presentations.
We consider the discrete, time-varying broadcast channel with memory under the assumption that the channel states belong to a set of finite cardinality. We first define the physically degraded finite-state broadcast channel for which we derive the capacity region. We then define the stochastically degraded finite-state broadcast channel and derive the capacity region for this scenario as well. In both scenarios we consider the non-indecomposable finite-state channel as well as the indecomposable one.
The capacity region of a broadcast channel consisting of k-receivers that lie in a less noisy sequence is an open problem, when k >= 3. We solve this problem for the case k=3. We prove that superposition coding is optimal for a class of broadcast channels with a sequence of less noisy receivers. T
Motivated by a simple broadcast channel, we generalize the notions of a less noisy receiver and a more capable receiver to an essentially less noisy receiver and an essentially more capable receiver respectively. We establish the capacity regions of these classes by borrowing on existing techniques to obtain the characterization of the capacity region for certain new and interesting classes of broadcast channels. We also establish the relationships between the new classes and the existing classes.
An outer bound to the capacity region of the two-receiver discrete memoryless broadcast channel is given. The outer bound is tight for all cases where the capacity region is known. When specialized to the case of no common information, this outer bound is contained in the Korner-Marton outer bound. This containment is shown to be strict for the binary skew-symmetric broadcast channel. Thus, this outer bound is in general tighter than all other known outer bounds on the discrete memoryless broadcast channel.
We develop a new method for showing the optimality of the Gaussian distribution in multiterminal information theory problems. As an application of this method we show that Marton's inner bound achieves the capacity of the vector Gaussian broadcast channels with common message.
We propose two coding schemes for discrete memoryless broadcast channels (DMBCs) with rate-limited feedback from only one receiver. For any positive feedback rate and for the class of strictly less-noisy DMBCs, our schemes strictly improve over the no-feedback capacity region.
We consider the problem of broadcast with common messages, and focus on the case that the common message rate $R_{\mathcal{A}}$, i.e., the rate of the message intended for all the receivers in the set $\mathcal{A}$, is the same for all the set $\mathcal{A}$ of the same cardinality. Instead of attempting to characterize the capacity region of general broadcast channels, we only consider the structure of the capacity region that any broadcast channel should bear. The concept of latent capacity region is useful in capturing these underlying constraints, and we provide a complete characterization …
We derive a new outer bound on the capacity region of broadcast traffic in multiple input broadcast packet erasure channels with feedback, and extend this outer bound to packet erasure relay networks with feedback. We show the tightness of the outer bound for various classes of networks. An important engineering implication of this work is that for network coding schemes for parallel broadcast channels, the `xor' packets should be sent over correlated broadcast subchannels.
The identification capacity region of the compound broadcast channel is determined under an average error criterion, where the sender has no channel state information. We give single-letter identification capacity formulas for discrete channels and multiple-input multiple-output Gaussian channels under an average input constraint. The capacity theorems apply to general discrete memoryless broadcast channels. This is in contrast to the transmission setting, where the capacity is only known for special cases, notably the degraded broadcast channel and the multiple-input multiple-output broadcast…
This paper considers a Gaussian broadcast channel with two unmatched degraded components, three particular messages, and a common message that is intended for all three receivers. It is shown that for this channel superposition coding and Gaussian signalling is sufficient to achieve every point in the capacity region.
This paper establishes the capacity region of a class of broadcast channels with random state in which each channel component is selected from two possible functions and each receiver knows its state sequence. This channel model does not fit into any class of broadcast channels for which the capacity region was previously known and is useful in studying wireless communication channels when the fading state is known only at the receivers. The capacity region is shown to coincide with the UV outer bound and is achieved via Marton coding.
We consider the discrete memoryless degraded broadcast channels. We prove that the error probability of decoding tends to one exponentially for rates outside the capacity region and derive an explicit lower bound of this exponent function. We shall demonstrate that the information spectrum approach is quite useful for investigating this problem.
We study broadcast capacity and minimum delay scaling laws for highly mobile wireless networks, in which each node has to disseminate or broadcast packets to all other nodes in the network. In particular, we consider a cell partitioned network under the simplified independent and identically distributed (IID) mobility model, in which each node chooses a new cell at random every time slot. We derive scaling laws for broadcast capacity and minimum delay as a function of the cell size. We propose a simple first-come-first-serve (FCFS) flooding scheme that nearly achieves both capacity and minimum…
In this paper, we investigate the problem of secure broadcasting over block-fading channels with limited channel knowledge at the transmitter. More particularly, we analyze the effect of having imperfect channel state information (CSI) via a finite rate feedback on the throughput of a broadcast channel where the transmission is intended for multiple legitimate receivers in the presence of an eavesdropper. First, we partially characterize the ergodic secrecy capacity of the system when the source broadcasts the same information to all the receivers, i.e., common message transmission. Then, we l…
We consider the broadcast phase of a three-node network, where a relay node establishes a bidirectional communication between two nodes using a spectrally efficient two-phase decode-and-forward protocol. In the first phase the two nodes transmit their messages to the relay node. Then the relay node decodes the messages and broadcasts a re-encoded composition of them in the second phase. We consider Gaussian MIMO channels and determine the capacity region for the second phase which we call the Gaussian MIMO bidirectional broadcast channel.
Korner and Marton established the capacity region for the 2-receiver broadcast channel with degraded message sets. Recent results and conjectures suggest that a straightforward extension of the Korner-Marton region to more than 2 receivers is optimal. This paper shows that this is not the case. We establish the capacity region for a class of 3-receiver broadcast channels with 2 degraded message sets and show that it can be strictly larger than the straightforward extension of the Korner-Marton region. The key new idea is indirect decoding, whereby a receiver who cannot directly decode a cloud …
We establish the capacity region of several classes of broadcast channels with random state in which the channel to each user is selected from two possible channel state components and the state is known only at the receivers. When the channel components are deterministic, we show that the capacity region is achieved via Marton coding. This channel model does not belong to any class of broadcast channels for which the capacity region was previously known and is useful in studying wireless communication channels when the fading state is known only at the receivers. We then establish the capacit…
Consider the broadcast relay channel (BRC) which consists of a source sending information over a two user broadcast channel in presence of two relay nodes that help the transmission to the destinations. Clearly, this network with five nodes involves all the problems encountered in relay and broadcast channels. New inner bounds on the capacity region of this class of channels are derived. These results can be seen as a generalization and hence unification of previous work in this topic. Our bounds are based on the idea of recombination of message bits and various effective coding strategies for…
In this paper, we investigate upper and lower bounds on the capacity of two-user fading broadcast channels where one of the users has a constant (non-fading) channel. We use the Costa entropy power inequality (EPI) along with an optimization framework to derive upper bounds on the sum-capacity and superposition coding to obtain lower bounds on the sum-rate for this channel. For this fading broadcast channel where one channel is constant, we find that the upper and lower bounds meet under special cases, and in general, we show that the achievable sum-rate comes within a constant of the outer bo…
In this paper, we study capacity bounds for discrete memoryless broadcast channels with confidential messages. Two private messages as well as a common message are transmitted; the common message is to be decoded by both receivers, while each private message is only for its intended receiver. In addition, each private message is to be kept secret from the unintended receiver where secrecy is measured by equivocation. We propose both inner and outer bounds to the rate equivocation region for broadcast channels with confidential messages. The proposed inner bound generalizes Csiszár and Körner's…
This paper focuses on the 1-to-K broadcast packet erasure channel (PEC), which is a generalization of the broadcast binary erasure channel from the binary symbol to that of arbitrary finite fields GF(q) with sufficiently large q. We consider the setting in which the source node has instant feedback of the channel outputs of the K receivers after each transmission. Such a setting directly models network coded packet transmission in the downlink direction with integrated feedback mechanisms (such as Automatic Repeat reQuest (ARQ)). The main results of this paper are: (i) The capacity region for …
It is well known that, in general, feedback may enlarge the capacity region of Gaussian broadcast channels. This has been demonstrated even when the feedback is noisy (or partial-but-perfect) and only from one of the receivers. The only case known where feedback has been shown not to enlarge the capacity region is when the channel is physically degraded (El Gamal 1978, 1981). In this paper, we show that for a class of two-user Gaussian broadcast channels (not necessarily physically degraded), passively feeding back the stronger user's signal over a link corrupted by Gaussian noise does not enl…
The fact that the results for 2-receiver broadcast channels (BCs) are not generalized to the 3-receiver ones is of information theoretical importance. In this paper we study two classes of discrete memoryless BCs with non-causal side information (SI), i.e. multilevel BC (MBC) and 3-receiver less noisy BC. First, we obtain an achievable rate region and a capacity outer bound for the MBC. Second, we prove a special capacity region for the 3-receiver less noisy BC. Third, the obtained special capacity region for the 3-receiver less noisy BC is extended to continuous alphabet fading Gaussian versi…
Despite considerable progress on the information-theoretic broadcast channel, the capacity region of fading broadcast channels with channel state known at the receivers but unknown at the transmitter remains unresolved. We address this subject by introducing a layered erasure broadcast channel model in which each component channel has a state that specifies the received signal levels in an instance of a deterministic binary expansion channel. We find the capacity region of this class of broadcast channels. The capacity achieving strategy assigns each signal level to the user that derives the m…
The wiretap channel model of Wyner is one of the first communication models with both reliability and security constraints. Capacity-achieving schemes for various models of the wiretap channel have received considerable attention in recent literature. In this paper, we show that capacity of the general (not necessarily degraded or symmetric) wiretap channel under a "strong secrecy constraint" can be achieved using a transmission scheme based on polar codes. We also extend our construction to the case of broadcast channels with confidential messages defined by Csisz{á}r and K{örner}, achieving …
Jolfaei et al. used feedback to create transmit signals that are simultaneously useful for multiple users in a broadcast channel. Later, Georgiadis and Tassiulas studied erasure broadcast channels with feedback, and presented the capacity region under certain assumptions. These results provided the fundamental ideas used in communication protocols for networks with delayed channel state information. However, to the best of our knowledge, the capacity region of erasure broadcast channels with feedback and with a common message for both receivers has never been presented. This latter problem sho…
In this paper, a class of broadcast interference channels (BIC) is investigated, where one of the two broadcast receivers is subject to interference coming from a point-to-point transmission. For a general discrete memoryless broadcast interference channel (DM-BIC), an achievable scheme based on message splitting, superposition and binning is proposed and a concise representation of the corresponding achievable rate region R is obtained. Two partial-order broadcast conditions interference-oblivious less noisy and interference-cognizant less noisy are defined, thereby extending the usual less n…
We provide an alternative proof for the capacity region of the degraded Gaussian multiple-input multiple-output (MIMO) broadcast channel. Our proof does not use the channel enhancement technique as opposed to the original proof of Weingertan {\it et. al.} and the alternative proof of Liu {\it et. al}. Our proof starts with the single-letter description of the capacity region of the degraded broadcast channel, and directly evaluates it for the degraded Gaussian MIMO broadcast channel by using two main technical tools. The first one is the generalized de Bruijn identity due to Palomar \emph{et. …
The compound broadcast channel with confidential messages (BCC) generalizes the BCC by modeling the uncertainty of the channel. For the compound BCC, it is only known that the actual channel realization belongs to a pre-specified uncertainty set of channels and that it is constant during the whole transmission. For reliable and secure communication is necessary to operate at a rate pair within the compound BCC capacity region. Therefore, the question whether small variations of the uncertainty set lead to large losses of the compound BCC capacity region is studied. It is shown that the compoun…
This paper investigates the capacity region of the optical intensity broadcast channels (OI-BCs), where the input is subject to a peak-intensity constraint, an average-intensity constraint, or both. By leveraging the decomposition results of several random variables, i.e., uniform, exponential, and truncated exponential random variables, and adopting a superposition coding (SC) scheme, the inner bound on the capacity region is derived. Then, the outer bound is derived by applying the conditional entropy power inequality (EPI). In the high signal-to-noise ratio (SNR) regime, the inner bound asy…
This paper focuses on the 1-to-K broadcast packet erasure channel (PEC), which is a generalization of the broadcast binary erasure channel from the binary symbol to that of arbitrary finite fields GF(q) with sufficiently large q. We consider the setting in which the source node has instant feedback of the channel outputs of the K receivers after each transmission. The capacity region of the 1-to-K PEC with COF was previously known only for the case K=2. Such a setting directly models network coded packet transmission in the downlink direction with integrated feedback mechanisms (such as Automa…
The fading broadcast channel with confidential messages (BCC) is investigated, where a source node has common information for two receivers (receivers 1 and 2), and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The channel state information (CSI) is assumed to be known at both the transmitter and the receivers. The secrecy capacity region is first established for the parallel Gaussian BCC, and the optimal source power allocations that achieve the boundary of the secrecy capacity region are derived…
A class of diamond networks is studied where the broadcast component is orthogonal and modeled by two independent bit-pipes. New upper and lower bounds on the capacity are derived. The proof technique for the upper bound generalizes bounding techniques of Ozarow for the Gaussian multiple description problem (1981) and Kang and Liu for the Gaussian diamond network (2011). The lower bound is based on Marton's coding technique and superposition coding. The bounds are evaluated for Gaussian and binary adder multiple access channels (MACs). For Gaussian MACs, both the lower and upper bounds strengt…
Classical multiuser information theory studies the fundamental limits of models with a fixed (often small) number of users as the coding blocklength goes to infinity. Motivated by emerging systems with a massive number of users, this paper studies the new {\em many-user paradigm}, where the number of users is allowed to grow with the blocklength. The focus of this paper is the degraded many-broadcast channel model, whose number of users may grow as fast as linearly with the blocklength. A notion of capacity in terms of message length is defined and an example of Gaussian degraded many-broadcas…
A coding scheme for the discrete memoryless broadcast channel with {noiseless, noisy, generalized} feedback is proposed, and the associated achievable region derived. The scheme is based on a block-Markov strategy combining the Marton scheme and a lossy version of the Gray-Wyner scheme with side-information. In each block the transmitter sends fresh data and update information that allows the receivers to improve the channel outputs observed in the previous block. For a generalization of Dueck's broadcast channel our scheme achieves the noiseless-feedback capacity, which is strictly larger tha…
The two-receiver broadcast packet erasure channel with feedback and memory is studied. Memory is modeled using a finite-state Markov chain representing a channel state. The channel state is unknown at the transmitter, but observations of this hidden Markov chain are available at the transmitter through feedback. Matching outer and inner bounds are derived and the capacity region is determined. The capacity region does not have a single-letter characterization and is, in this sense, uncomputable. Approximations of the capacity region are provided and two optimal coding algorithms are outlined. …
This paper investigates the capacity regions of two-receiver broadcast channels where each receiver (i) has both common and private-message requests, and (ii) knows part of the private message requested by the other receiver as side information. We first propose a transmission scheme and derive an inner bound for the two-receiver memoryless broadcast channel. We next prove that this inner bound is tight for the deterministic channel and the more capable channel, thereby establishing their capacity regions. We show that this inner bound is also tight for all classes of two-receiver broadcast ch…
We formulate and study a cryptographic problem relevant to wireless: a sender, Alice, wants to transmit private messages to two receivers, Bob and Calvin, using unreliable wireless broadcast transmissions and short public feedback from Bob and Calvin. We ask, at what rates can we broadcast the private messages if we also provide (information-theoretic) unconditional security guarantees that Bob and Calvin do not learn each-other's message? We characterize the largest transmission rates to the two receivers, for any protocol that provides unconditional security guarantees. We design a protocol …
The two-user computation broadcast problem is introduced as the setting where User $1$ wants message $W_1$ and has side-information $W_1'$, User $2$ wants message $W_2$ and has side-information $W_2'$, and $(W_1, W_1', W_2, W_2')$ may have arbitrary dependencies. The rate of a computation broadcast scheme is defined as the ratio $H(W_1,W_2)/H(S)$, where $S$ is the information broadcast to both users to simultaneously satisfy their demands. The supremum of achievable rates is called the capacity of computation broadcast $C_{CB}$. It is shown that $C_{CB}\leq H(W_1,W_2)/\left[H(W_1|W_1')+H(W_2|W…
In a broadcast channel with random packet arrival and transmission queues, the stability of the system is achieved by maximizing a weighted sum rate capacity with suitable weights that depend on the queue size. The weighted sum rate capacity using Dirty Paper Coding (DPC) and Zero Forcing (ZF) is asymptotically equivalent to the weighted sum capacity over parallel single-channels. In this paper, we study the Diversity Multiplexing Tradeoff (DMT) of the fading broadcast channel under a fixed weighted sum rate capacity constraint. The DMT of both identical and different parallel weighted MISO ch…
We derive the capacity region of the state-dependent semideterministic broadcast channel with noncausal state-information at the transmitter. One of the two outputs of this channel is a deterministic function of the channel input and the channel state, and the state is assumed to be known noncausally to the transmitter but not to the receivers. We show that appending the state to the deterministic output does not increase capacity. We also derive an outer bound on the capacity of general (not necessarily semideterministic) state-dependent broadcast channels.
We derive universal codes for transmission of broadcast and confidential messages over classical-quantum-quantum and fully quantum channels. These codes are robust to channel uncertainties considered in the compound model. To construct these codes we generalize random codes for transmission of public messages, to derive a universal superposition coding for the compound quantum broadcast channel. As an application, we give a multi-letter characterization of regions corresponding to the capacity of the compound quantum broadcast channel for transmitting broadcast and confidential messages simult…
The present paper focuses on the problem of broadcasting information in the most efficient manner in a large two-dimensional ad hoc wireless network at low SNR and under line-of-sight propagation. A new communication scheme is proposed, where source nodes first broadcast their data to the entire network, despite the lack of sufficient available power. The signal's power is then reinforced via successive back-and-forth beamforming transmissions between different groups of nodes in the network, so that all nodes are able to decode the transmitted information at the end. This scheme is shown to a…
We study the two-user Gaussian multiple-input multiple-output (MIMO) broadcast channel with common and confidential messages. In this channel, the transmitter sends a common message to both users, and a confidential message to each user which is kept perfectly secret from the other user. We obtain the entire capacity region of this channel. We also explore the connections between the capacity region we obtained for the Gaussian MIMO broadcast channel with common and confidential messages and the capacity region of its non-confidential counterpart, i.e., the Gaussian MIMO broadcast channel with…
Recent research indicates that packet transmission employing random linear network coding can be regarded as transmitting subspaces over a linear operator channel (LOC). In this paper we propose the framework of linear operator broadcast channels (LOBCs) to model packet broadcasting over LOCs, and we do initial work on the capacity region of constant-dimension multiplicative LOBCs(CMLOBCs), a generalization of broadcast erasure channels. Two fundamental problems regarding CMLOBCs are addressed-finding necessary and sufficient conditions for degradation and deciding whether time sharing suffice…
The two-receiver broadcast packet erasure channel with feedback and memory is studied. Memory is modeled using a finite-state Markov chain representing a channel state. Outer and inner bounds on the capacity region are derived when the channel state is strictly causally known at the transmitter. The bounds are both formulated in terms of feasibility problems and they are matching in all but one of the constraints. The results are extended to feedback with larger delay. Numerical results show that the bounds are close in many examples and the gains offered through feedback can be quite large. T…
This paper provides an explicit expression for the capacity region of the two-user broadcast Z channel and proves that the optimal boundary can be achieved by independent encoding of each user. Specifically, the information messages corresponding to each user are encoded independently and the OR of these two encoded streams is transmitted. Nonlinear turbo codes that provide a controlled distribution of ones and zeros are used to demonstrate a low-complexity scheme that operates close to the optimal boundary.
In wireless distributed storage systems, storage nodes are connected by wireless channels, which are broadcast in nature. This paper exploits this unique feature to design an efficient repair mechanism, called broadcast repair, for wireless distributed storage systems in the presence of multiple-node failures. Due to the broadcast nature of wireless transmission, we advocate a new measure on repair performance called repair-transmission bandwidth. In contrast to repair bandwidth, which measures the average number of packets downloaded by a newcomer to replace a failed node, repair-transmission…
We investigate the effects of an additional relay node on the secrecy of broadcast channels by considering the model of relay broadcast channels with confidential messages. We show that this additional relay node can increase the achievable secrecy rate region of the broadcast channels with confidential messages. More specifically, first, we investigate the discrete memoryless relay broadcast channels with two confidential messages and one common message. Three inner bounds (with respect to decode-forward, generalized noise-forward and compress-forward strategies) and an outer bound on the cap…
This work investigates the secrecy capacity of the Wiretap Broadcast Channel (WBC) with an external eavesdropper where a source wishes to communicate two private messages over a Broadcast Channel (BC) while keeping them secret from the eavesdropper. We derive a non-trivial outer bound on the secrecy capacity region of this channel which, in absence of security constraints, reduces to the best known outer bound to the capacity of the standard BC. An inner bound is also derived which follows the behavior of both the best known inner bound for the BC and the Wiretap Channel. These bounds are show…
The relay broadcast channel (RBC) is considered, in which a transmitter communicates with two receivers with the assistance of a relay. Based on different degradation orders among the relay and the receivers' outputs, three types of physically degraded RBCs (PDRBCs) are introduced. Inner bounds and outer bounds are derived on the capacity region of the presented three types. The bounds are tight for two types of PDRBCs: 1) one receiver's output is a degraded form of the other receiver's output, and the relay's output is a degraded form of the weaker receiver's output; 2) one receiver's output …
In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers via a Gaussian MIMO broadcast channel. A wire-tapper also receives the transmitted signal via another MIMO channel. It is assumed that the channels are degraded and the wire-tapper has the worst channel. We establish the capacity region of this scenario. Our achievability scheme is a combination of the superposition of Gaussian codes and randomization within the layers which we will refer to as Secret Superposition Coding. For the outerbound, we use the notion of…
In this work, we study the arbitrarily varying broadcast channel (AVBC), when state information is available at the transmitter in a causal manner. We establish 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 informations between the strategy variables and the channel outputs. As an example, we consider the arbitrarily varying binary symmetric broadcast channel with correlated noises. We show cases where the co…
