We study the best known general inner bound[MAR '79] and outer bound[N-EG'07] for the capacity region of the two user discrete memory less channel. We prove that a seemingly stronger outer bound is identical to a weaker form of the outer bound that was also presented in [N-EG'07]. We are able to further express the best outer bound in a form that is computable, i.e. there are bounds on the cardinalities of the auxiliary random variables.
The inner and outer bounds coincide for all channels for which the capacity region is known and it is not known whether the regions described by these bounds are same or different. We present a channel, where assuming a certain conjecture backed by simulations and partial theoretical results, one can show that the bounds are different.
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.
We study a class of discrete memoryless broadcast interference channels (DM-BICs), where one of the broadcast receivers is subject to the interference from a point-to-point transmission. A general achievable rate region $\mathcal{R}$ based on rate splitting, superposition coding and binning at the broadcast transmitter and rate splitting at the interfering transmitter is derived. Under two partial order broadcast conditions {\em interference-oblivious less noisy} and {\em interference-cognizant less noisy}, a reduced form of $\mathcal{R}$ is shown to be equivalent to the region based on a simp…
A memoryless state-dependent broadcast channel (BC) is considered, where the transmitter wishes to convey two private messages to two receivers while simultaneously estimating the respective states via generalized feedback. The model at hand is motivated by a joint radar and communication system where radar and data applications share the same frequency band. For physically degraded BCs with i.i.d. state sequences, we characterize the capacity-distortion tradeoff region. For general BCs, we provide inner and outer bounds on the capacitydistortion region, as well as a sufficient condition when …
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…
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 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…
We study information-theoretic security for discrete memoryless interference and broadcast channels with independent confidential messages sent to two receivers. Confidential messages are transmitted to their respective receivers with information-theoretic secrecy. That is, each receiver is kept in total ignorance with respect to the message intended for the other receiver. The secrecy level is measured by the equivocation rate at the eavesdropping receiver. In this paper, we present inner and outer bounds on secrecy capacity regions for these two communication systems. The derived outer bound…
We consider the two-receiver memoryless broadcast channel with states where each receiver requests both common and private messages, and may know part of the private message requested by the other receiver as receiver message side information (RMSI). We address two categories of the channel (i) channel with states known causally to the transmitter, and (ii) channel with states known non-causally to the transmitter. Starting with the channel without RMSI, we first propose a transmission scheme and derive an inner bound for the causal category. We then unify our inner bound for the causal catego…
We derive upper and lower bounds on the reliability function for the common-message discrete memoryless broadcast channel with variable-length feedback. We show that the bounds are tight when the broadcast channel is stochastically degraded. For the achievability part, we adapt Yamamoto and Itoh's coding scheme by controlling the expectation of the maximum of a set of stopping times. For the converse part, we adapt Burnashev's proof techniques for establishing the reliability functions for (point-to-point) discrete memoryless channels with variable-length feedback and sequential hypothesis tes…
This paper investigates the joint source-channel coding problem of sending a memoryless source over a memoryless broadcast channel. An inner bound and several outer bounds on the admissible distortion region are derived, which respectively generalize and unify several existing bounds. As a consequence, we also obtain an inner bound and an outer bound for the degraded broadcast channel case. When specialized to the Gaussian or binary source broadcast, the inner bound and outer bound not only recover the best known inner bound and outer bound in the literature, but also generate some new results…
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.
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
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…
A $K$-user memoryless interference channel is considered where each receiver sequentially decodes the data of a subset of transmitters before it decodes the data of the designated transmitter. Therefore, the data rate of each transmitter depends on (i) the subset of receivers which decode the data of that transmitter, (ii) the decoding order, employed at each of these receivers. In this paper, a greedy algorithm is developed to find the users which are decoded at each receiver and the corresponding decoding order such that the minimum rate of the users is maximized. It is proven that the propo…
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…
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 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.
The capacity of a time-varying block-memoryless channel in which the transmitter and the receiver have access to (possibly different) noisy causal channel side information (CSI) is obtained. It is shown that the capacity formula obtained in this correspondence reduces to the capacity formula reported in \cite{Gold07} for the special case where the transmitter CSI is a deterministic function of the receiver CSI.
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…
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 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 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…
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 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…
We study the problem of coding over a general discrete memoryless broadcast channel controlled by random parameters. The parameters are available at the transmitter in a non-causal manner and are subject to a state masking constraint on the receivers. We derive inner and outer bounds on the achievable region and show that for the special case of Gaussian broadcast channel with private messages, these bounds are tight.
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 study the finite blocklength limits of state-dependent discrete memoryless channels where the discrete memoryless state is known noncausally at the encoder. For the point-to-point case, this is known as the Gel'fand-Pinsker channel model. We define the (n,ε)-capacity of the Gel'fand-Pinsker channel as the maximal rate of transmission of a message subject to the condition that the length of the block-code is n and the average error probability is no larger than ε. This paper provides a lower bound for the (n,ε)-capacity of the Gel'fand-Pinsker channel model, and hence an upper…
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 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.
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.
A coding scheme is proposed for the memoryless Gaussian broadcast channel with correlated noises and feedback. For all noise correlations other than -1, the gap between the sum-rate the scheme achieves and the full-cooperation bound vanishes as the signal-to-noise ratio tends to infinity. When the correlation coefficient is -1, the gains afforded by feedback are unbounded and the prelog is doubled. When the correlation coefficient is +1 we demonstrate a dichotomy: If the noise variances are equal, then feedback is useless, and otherwise, feedback affords unbounded rate gains and doubles the pr…
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…
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 …
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…
We consider a discrete memoryless broadcast channel consists of two users and a sender. The sender has two independent confidential messages for each user. We extend the work of Liu et al.\ on broadcast channels with two confidential messages with weak secrecy criterion to strong secrecy. Our results are based on an extension of the techniques developed by Hou and Kramer on bounding Kullback-Leibler divergence in context of \textit{resolvability} and \textit{effective secrecy}.
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…
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 …
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…
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.
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 c…
Achievable rate regions for cooperative relay broadcast channels with rate-limited feedback are proposed. Specifically, we consider two-receiver memoryless broadcast channels where each receiver sends feedback signals to the transmitter through a noiseless and rate-limited feedback link, and meanwhile, acts as relay to transmit cooperative information to the other receiver. It's shown that the proposed rate regions improve on the known regions that consider either relaying cooperation or feedback communication, but not both.
This paper considers the three-receiver AWGN broadcast channel where the receivers (i) have private-message requests and (ii) know some of the messages requested by other receivers as side information. For this setup, all possible side information configurations have been recently classified into eight groups and the capacity of the channel has been established for six groups (Asadi et al., ISIT 2014). We propose inner and outer bounds for the two remaining groups, groups 4 and 7. A distinguishing feature of these two groups is that the weakest receiver knows the requested message of the stron…
We study private broadcasting of two messages to two groups of receivers over independent parallel channels. One group consists of an arbitrary number of receivers interested in a common message, whereas the other group has only one receiver. Each message must be kept confidential from the receiver(s) in the other group. Each of the sub-channels is degraded, but the order of receivers on each channel can be different. While corner points of the capacity region were characterized in earlier works, we establish the capacity region and show the optimality of a superposition strategy. For the case…
We study the transmission of confidential messages across a wireless broadcast channel with K>2 receivers and K helpers. The goal is to transmit all messages reliably to their intended receivers while keeping them confidential from the unintended receivers. We design a codebook based on nested lattice structure, cooperative jamming, lattice alignment, and i.i.d. coding. Moreover, we exploit the asymmetric compute-and-forward decoding strategy to handle finite SNR regimes. Unlike previous alignment schemes, our achievable rates are attainable at any finite SNR value. Also, we show that our sche…
This paper investigates the capacity region of the three-receiver AWGN broadcast channel where the receivers (i) have private-message requests and (ii) may know some of the messages requested by other receivers as side information. We first classify all 64 possible side information configurations into eight groups, each consisting of eight members. We next construct transmission schemes, and derive new inner and outer bounds for the groups. This establishes the capacity region for 52 out of 64 possible side information configurations. For six groups (i.e., groups 1, 2, 3, 5, 6, and 8 in our te…
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…
