We consider a broadcast channel with 3 receivers and 2 messages (M0, M1) where two of the three receivers need to decode messages (M0, M1) while the remaining one just needs to decode the message M0. We study the best known inner and outer bounds under this setting, in an attempt to find the deficiencies with the current techniques of establishing the bounds. We produce a simple example where we are able to explicitly evaluate the inner bound and show that it differs from the general outer bound. For a class of channels where the general inner and outer bounds differ, we use a new argument to show that the inner bound is tight.
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.
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 consider the discrete memoryless degraded broadcast channels with feedback. 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.
Machine learning has shown promising results for communications system problems. We present results on the use of deep auto-encoders in order to learn a transceiver for the multiuser degraded broadcast channel, and see that the auto encoder is able to learn to communicate on this channel using superposition coding. Additionally, the deep neural net is able to determine a bit labeling and optimize the per user power allocation that depends on the per user SNR.
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…
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. …
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 …
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 …
Different polar coding schemes are proposed for the memoryless degraded broadcast channel under different reliability and secrecy requirements: layered decoding and/or layered secrecy. In this setting, the transmitter wishes to send multiple messages to a set of legitimate receivers keeping them masked from a set of eavesdroppers. The layered decoding structure requires receivers with better channel quality to reliably decode more messages, while the layered secrecy structure requires eavesdroppers with worse channel quality to be kept ignorant of more messages. The implementation of the propo…
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…
In this paper, first, we investigate the model of degraded broadcast channel with side information and confidential messages. This work is from Steinberg's work on the degraded broadcast channel with causal and noncausal side information, and Csisz$\acute{a}$r-Körner's work on broadcast channel with confidential messages. Inner and outer bounds on the capacity-equivocation regions are provided for the noncausal and causal cases. Superposition coding and double-binning technique are used in the corresponding achievability proofs. Then, we investigate the degraded broadcast channel with side inf…
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…
Error and erasure exponents for the broadcast channel with degraded message sets are analyzed. The focus of our error probability analysis is on the main receiver where, nominally, both messages are to be decoded. A two-step decoding algorithm is proposed and analyzed. This receiver first attempts to decode both messages, failing which, it attempts to decode only the message representing the coarser information, i.e., the cloud center. This algorithm reflects the intuition that we should decode both messages only if we have confidence in the estimates; otherwise one should only decode the coar…
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…
As demonstrated in many recent studies, cooperation between users can greatly improve the performance of communication systems. Most of the works in the literature present models where all the users are aware of the resources available for cooperation. However, the scenario where cooperation links are sometimes unavailable or that some users cannot be updated whether the cooperation links are present or not, is more realistic in today's dynamic ad-hoc communication systems. In such a case we need coding schemes that exploit the cooperation links if they are present, and can still operate if co…
A new non-orthogonal multiple access scheme performing simultaneous transmission to multiple users characterized by different signal-to-noise ratios is proposed. Different users are multiplexed by storing their codewords into a multiplexing matrix according to properly designed patterns and then mapping the columns of the matrix onto the symbols of a higher-order constellation. At the receiver, an interference cancellation algorithm is employed in order to achieve a higher spectral efficiency than orthogonal user multiplexing. Rate-Adaptive Constellation Expansion Multiple Access (RA-CEMA) is …
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…
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 two-receiver discrete memoryless broadcast channel is presented. We compare it to the known outer bounds and show that the outer bound presented is at least as tight as the existing bounds.
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
A state-dependent degraded broadcast diamond channel is studied where the source-to-relays cut is modeled with two noiseless, finite-capacity digital links with a degraded broadcasting structure, while the relays-to-destination cut is a general multiple access channel controlled by a random state. It is assumed that the source has non-causal channel state information and the relays have no state information. Under this model, first, the capacity is characterized for the case where the destination has state information, i.e., has access to the state sequence. It is demonstrated that in this cas…
This paper studies the problem of secure communcation over the two-receiver discrete memoryless broadcast channel with one-sided receiver side information and with a passive eavesdropper. We proposed a coding scheme which is based upon the superposition-Marton framework. Secrecy techniques such as the one-time pad, Carleial-Hellman secrecy coding and Wyner serecy coding are applied to ensure individual secrecy. This scheme is shown to be capacity achieving for some cases of the degraded broadcast channel. We also notice that one-sided receiver side information provides the advantage of rate re…
We consider scheduled message communication over a discrete memoryless degraded broadcast channel. The framework we consider here models both the random message arrivals and the subsequent reliable communication by suitably combining techniques from queueing theory and information theory. The channel from the transmitter to each of the receivers is quasi-static, flat, and with independent fades across the receivers. Requests for message transmissions are assumed to arrive according to an i.i.d. arrival process. Then, (i) we derive an outer bound to the region of message arrival vectors achieva…
A discrete memoryless half-duplex relay channel is constructed from a broadcast channel from the source to the relay and destination and a multiple access channel from the source and relay to the destination. When the relay listens, the channel operates in the broadcast mode. The channel switches to the multiple access mode when the relay transmits. If the broadcast component channel is physically degraded, the half-duplex relay channel will also be referred to as physically degraded. The capacity of this degraded half-duplex relay channel is examined. It is shown that the block Markov coding …
Consider a memoryless degraded broadcast channel (DBC) in which the channel output is a single-letter function of the channel input and the channel noise. As examples, for the Gaussian broadcast channel (BC) this single-letter function is regular Euclidian addition and for the binary-symmetric BC this single-letter function is Galois-Field-two addition. This paper identifies several classes of discrete memoryless DBCs for which a relatively simple encoding scheme, which we call natural encoding, achieves capacity. Natural Encoding (NE) combines symbols from independent codebooks (one for each …
In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wire-tapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by equivocation rate at the eavesdropper. We first study the general (non-degraded) broadcast channel with confidential messages. We present an inner bound on the secrecy capacity region for this model. The inner …
In this paper, bounds to the rate-equivocation region for the general 3-receiver broadcast channel (BC) with degraded message sets, are presented for confidential messages to be kept secret from one of the receivers. This model is more general than the 2-receiver BCs with confidential messages with an external wiretapper, and the recently studied 3-receiver degraded BCs with confidential messages, since in the model studied in this paper, the conditions on the receivers are general and the wiretapper receives the common message. Wyner's code partitioning combined with double-binning is used to…
We study noisy broadcast networks with local cache memories at the receivers, where the transmitter can pre-store information even before learning the receivers' requests. We mostly focus on packet-erasure broadcast networks with two disjoint sets of receivers: a set of weak receivers with all-equal erasure probabilities and equal cache sizes and a set of strong receivers with all-equal erasure probabilities and no cache memories. We present lower and upper bounds on the capacity-memory tradeoff of this network. The lower bound is achieved by a new joint cache-channel coding idea and significa…
A partially cooperative relay broadcast channel (RBC) is a three-node network with one source node and two destination nodes (destinations 1 and 2) where destination 1 can act as a relay to assist destination 2. Inner and outer bounds on the capacity region of the discrete memoryless partially cooperative RBC are obtained. When the relay function is disabled, the inner and outer bounds reduce to new bounds on the capacity region of broadcast channels. Four classes of RBCs are studied in detail. For the partially cooperative RBC with degraded message sets, inner and outer bounds are obtained. F…
We establish the deterministic-code capacity region of a network with one transmitter and two receivers: an "ordinary receiver" and a "robust receiver." The channel to the ordinary receiver is a given (known) discrete memoryless channel (DMC), whereas the channel to the robust receiver is an arbitrarily varying channel (AVC). Both receivers are required to decode the "common message," whereas only the ordinary receiver is required to decode the "private message."
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.
Three-receiver broadcast channel (BC) is of interest due to its information theoretical differences with two receiver one. In this paper, we derive achievable rate regions for two classes of 3-receiver BC with side information available at the transmitter, Multilevel BC and 3-receiver less noisy BC, by using superposition coding, Gel'fand-Pinsker binning scheme and Nair-El Gamal indirect decoding. Our rate region for multilevel BC subsumes the Steinberg rate region for 2-receiver degraded BC with side information as its special case. We also find the capacity region of 3-receiver less noisy BC…
We consider the transmission of classical information through a degraded broadcast channel, whose outputs are two quantum systems, with the state of one being a degraded version of the other. Yard et al. proved that the capacity region of such a channel is contained in a region characterized by certain entropic quantities. We prove that this region satisfies the strong converse property, that is, the maximal probability of error incurred in transmitting information at rates lying outside this region converges to one exponentially in the number of uses of the channel. In establishing this resul…
The problem of characterizing the capacity region for Gaussian broadcast channels with receiver message side information appears difficult and remains open for N >= 3 receivers. This paper proposes a joint network and Gelfand-Pinsker coding method for 3-receiver cases. Using the method, we establish a unified inner bound on the capacity region of 3-receiver Gaussian broadcast channels under general message side information configuration. The achievability proof of the inner bound uses an idea of joint interference cancelation, where interference is canceled by using both dirty-paper coding at …
This paper establishes inner bounds on the secrecy capacity regions for the general 3-receiver broadcast channel with one common and one confidential message sets. We consider two setups. The first is when the confidential message is to be sent to two receivers and kept secret from the third receiver. Achievability is established using indirect decoding, Wyner wiretap channel coding, and the new idea of generating secrecy from a publicly available superposition codebook. The inner bound is shown to be tight for a class of reversely degraded broadcast channels and when both legitimate receivers…
The secrecy capacity region for the K-receiver degraded broadcast channel (BC) is given for confidential messages sent to the receivers and to be kept secret from an external wiretapper. Superposition coding and Wyner's random code partitioning are used to show the achievable rate tuples. Error probability analysis and equivocation calculation are also provided. In the converse proof, a new definition for the auxiliary random variables is used, which is different from either the case of the 2-receiver BC without common message or the K-receiver BC with common message, both with an external wir…
We consider achieving the rates in the capacity region of a multi-level 3-receiver broadcast channel, in which the second receiver is degraded with respect to the first receiver, with degraded message sets. We propose a two-level chaining strategy based on polar codes that achieves the capacity region of the considered setting without time-sharing. We also look at a slight variation of this problem, where the first receiver only requires to decode its own private message and the other two receivers require to decode another private message common to them. We observe that the capacity region do…
This paper considers the problem of the multiple-input multiple-output (MIMO) Gaussian broadcast channel with two receivers (receivers 1 and 2) and two messages: a common message intended for both receivers and a confidential message intended only for receiver 1 but needing to be kept asymptotically perfectly secure from receiver 2. A matrix characterization of the secrecy capacity region is established via a channel enhancement argument. The enhanced channel is constructed by first splitting receiver 1 into two virtual receivers and then enhancing only the virtual receiver that decodes the co…
This paper investigates the capacity region of three-receiver AWGN broadcast channels where the receivers (i) have private-message requests and (ii) know the messages requested by some other receivers as side information. We classify these channels based on their side information into eight groups, and construct different transmission schemes for the groups. For six groups, we characterize the capacity region, and show that it improves both the best known inner and outer bounds. For the remaining two groups, we improve the best known inner bound by using side information during channel decodin…
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 involv…
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…
This letter investigates the role of index coding in the capacity of AWGN broadcast channels with receiver message side information. We first show that index coding is unnecessary where there are two receivers; multiplexing coding and superposition coding are sufficient to achieve the capacity region. We next show that, for more than two receivers, multiplexing coding and superposition coding alone can be suboptimal. We give an example where these two coding schemes alone cannot achieve the capacity region, but adding index coding can. This demonstrates that, in contrast to the two-receiver ca…
In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages to two receivers, while a wire-tapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by the equivocation rate at the eavesdropper. We first study the general (non-degraded) broadcast channel with an eavesdropper. We present an inner bound on the secrecy capacity region for this model. This inner bound is base…
Three-Receiver broadcast channels (BC) are of interest due to their information-theoretic differences with two-receiver one. In this paper, we derive achievable rate regions for two classes of 3-receiver BC with side information (SI), i.e. Multilevel BC (MBC) and 3-receiver less noisy BC, using a combination of superposition coding, Gelfand-Pinsker binning scheme and Nair-El Gamal indirect decoding. Our rate region for MBC subsumes Steinberg rate region for 2-receiver degraded BC with SI as its special case. We will also show that the obtained achievable rate regions in the first two cases are…
We consider a broadcast channel with a degraded message set, in which a single transmitter sends a common message to two receivers and a private message to one of the receivers only. The main goal of this work is to find new lower bounds to the error exponents of the strong user, the one that should decode both messages, and of the weak user, that should decode only the common message. Unlike previous works, where suboptimal decoders where used, the exponents we derive in this work pertain to optimal decoding and depend on both rates. We take two different approaches. The first approach is bas…
This paper studies pliable index coding, in which a sender broadcasts information to multiple receivers through a shared broadcast medium, and the receivers each have some message a priori and want any message they do not have. An approach, based on receivers that are absent from the problem, was previously proposed to find lower bounds on the optimal broadcast rate. In this paper, we introduce new techniques to obtained better lower bounds, and derive the optimal broadcast rates for new classes of the problems, including all problems with up to four absent receivers.
In general, the different links of a broadcast channel may experience different fading dynamics and, potentially, unequal or hybrid channel state information (CSI) conditions. The faster the fading and the shorter the fading block length, the more often the link needs to be trained and estimated at the receiver, and the more likely that CSI is stale or unavailable at the transmitter. Disparity of link fading dynamics in the presence of CSI limitations can be modeled by a multi-user broadcast channel with both non-identical link fading block lengths as well as dissimilar link CSIR/CSIT conditio…
This paper simplifies an existing coding scheme for the two-receiver discrete memoryless broadcast channel with complementary receiver side information where there is a passive eavesdropper and individual secrecy is required. The existing coding scheme is simplified in two steps by replacing Wyner secrecy coding with Carleial-Hellman secrecy coding. The resulting simplified scheme is free from redundant message splits and random components. Not least, the simplified scheme retains the existing achievable individual secrecy rate region. Finally, its construction simplicity helps us gain additio…
This work discusses the source broadcasting problem, i.e. transmitting a source to many receivers via a broadcast channel. The optimal rate-distortion region for this problem is unknown. The separation approach divides the problem into two complementary problems: source successive refinement and broadcast channel transmission. We provide bounds on the loss incorporated by applying time-sharing and separation in source broadcasting. If the broadcast channel is degraded, it turns out that separation-based time-sharing achieves at least a factor of the joint source-channel optimal rate, and this …
The recent commercial trends towards using smaller dish antennas for satellite receivers, and the growing density of broadcasting satellites, necessitate the application of robust adjacent satellite interference (ASI) cancellation schemes. This orbital density growth along with the wider beamwidth of a smaller dish have imposed an overloaded scenario at the satellite receiver, where the number of transmitting satellites exceeds the number of receiving elements at the dish antenna. To ensure successful operation in this practical scenario, we propose a satellite receiver that enhances signal de…
A cache-aided broadcast network is studied, in which a server delivers contents to a group of receivers over a packet erasure broadcast channel (BC). The receivers are divided into two sets with regards to their channel qualities: the weak and strong receivers, where all the weak receivers have statistically worse channel qualities than all the strong receivers. The weak receivers, in order to compensate for the high erasure probability they encounter over the channel, are equipped with cache memories of equal size, while the receivers in the strong set have no caches. Data can be pre-delivere…
It is known that, as opposed to point-to-point channel, separate source and channel coding is not optimal in general for sending correlated sources over multiuser channels. In some works joint source-channel coding has been investigated for some certain multiuser channels; i.g., multiple access channel (MAC) and broadcast channel (BC). In this paper, we obtain a sufficient condition for transmitting arbitrarily correlated sources over a discrete memoryless BC with cooperating receivers, where the receivers are allowed to exchange messages via a pair of noisy cooperative links. It is seen that …
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…
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…
