A novel class of achievable rate regions is obtained for the general$K$-receiver discrete memoryless broadcast channel over which two groupcast messages are to be transmitted, with each message required by an arbitrary group of receivers. The associated achievability schemes are parameterized by an expansion of the message set which then determines how random coding techniques are employed. These techniques include generalized versions of up-set message-splitting, the generation of possibly multiple auxiliary codebooks for certain compositions of split messages using superposition coding with subset inclusion order, partial interference decoding at all receivers in general, joint unique decoding at receivers that desire both messages, and non-unique or indirect decoding at receivers that desire only one of the two messages. The generality of the proposed class of schemes implies new achievable rate regions for problems previously not considered as well as those that were studied before, with specific members of that class having rate regions that coincide with previously found capacity regions for special classes of broadcast channels with two private or two nested groupcast messages, wherein the group of receivers desiring one message is contained in that desiring the other. Moreover, new capacity results are established for certain partially ordered classes of broadcast channels for a class of two non-nested groupcast messages. To further show the strength of the proposed achievable rate regions we consider the so-called combination network as a test case. When specialized to the combination network, some members of the class of inner bounds are shown, via converse results, to result in the capacity region when the two messages are (a) intended for two distinct sets of$K{-}1$receivers each and (b) nested, in which one message is intended for one or two (common) receivers and both messages are intended for all other (private) receivers. In the latter two nested messages cases, we hence recover, in a top-down manner, previous results by Bidokhti, Prabhakaran, and Diggavi, obtained therein using lower complexity network coding schemes based on rate-splitting and linear superposition coding but tailored to the combination network, while in the first case we obtain a new capacity result for a non-nested message set, which was hitherto unknown. Furthermore, we show the achievability of rate pairs in two interesting examples of combination networks, with three and four common receivers each. These examples were proposed in the previous literature to show the sub-optimality of the aforementioned rate-splitting and linear superposition coding scheme, and hence to motivate the additional consideration of a pre-encoding technique and a block-Markov linear superposition coding for the combination network, with the latter then lifted to the general broadcast channel. Our results suggest that the proposed framework here for the general broadcast channel when specialized to the combination network is strong enough to incorporate the enhancements afforded by those two latter techniques, thereby implying that perhaps block-Markov superposition coding is not necessary in the general broadcast channel. Moreover, there is a trade-off between the complexity of the coding scheme within the class of schemes we propose when applied to the combination network and that of the determination of the distribution of the auxiliary random variables and the encoding function that achieve the capacity region. This may have interesting implications for the general broadcast channel as well.

Multiple groupcasting over the broadcast channel (BC) is studied in a special setting. In particular, an inner bound is obtained for the$K$-receiver discrete memoryless (DM) BC for the diamond message set which consists of four groupcast messages: one desired by all receivers, one by all but two receivers, and two more desired by all but each one of those two receivers. The inner bound is based on rate-splitting and superposition coding and is given in explicit form herein as a union over coding distributions of four-dimensional polytopes. This inner bound is then shown to be the capacity for a certain class of partially ordered DM BCs with order defined via the less noisy condition. When specialized to the so- called combination network, which is a class of three-layer (two-hop) broadcast networks parameterized by$2^{K}{-}1$finite-and-arbitrary-capacity noiseless links from the source node in the first layer to as many nodes of the second layer, our top-down approach from the DM BC to the combination network yields an explicit inner bound as a single polytope via the identification of a single coding distribution. This inner bound consists of inequalities which are then identified to be within the class of generalized cut-set outer bounds recently obtained by Salimi et al for broadcast networks. We hence establish the capacity region of the general$K$-user combination network for the diamond message set, and do so in explicit and structured form. Such a result implies a certain strength of our inner bound for the DM BC in that it (a) produces a hitherto unknown capacity region when specialized to the combination network and (b) may capture many combinatorial aspects of the capacity region of the$K$-receiver DM BC itself for the diamond message set. Moreover, we extend that inner bound by adding binning to it. As in the no-binning case, we provide the more general inner bound in explicit form.

This paper investigates the three-receiver (Y1, Y2, Y3) discrete memoryless (DM) broadcast channel (BC) for eight receive message cognition settings in which the weakest receiver Y3knows the message intended for the intermediate receiver Y2, Y2may or may not know the message intended for Y3, and the strongest receiver Y1knows none, one, or both of the messages intended for receivers Y2and Y3. For these eight settings, but for the Gaussian BC, the capacity regions were obtained previously by Asadi et al. In this paper, we establish the capacity regions for all eight cases for the class of less noisy DM BCs, thereby lifting the previously known capacity results from the Gaussian BC to the less noisy BC. To further expand the optimality results to strictly larger classes of broadcast channels, we propose a coding scheme that includes rate-splitting and indirect decoding, techniques not needed for the less noisy or Gaussian BCs, for four of the eight message cognition cases in which receiver Y2knows the message intended for Y3, and show that this more general scheme achieves capacity without requiring that receiver Y2be stronger than Y3in any sense (and when Y1knows the message intended for Y2, Y1is not required to be stronger than Y2either whereas when Y1does not know the message intended for Y2it is assumed that Y1is more capable than Y2) whereas it is assumed that Y1is less noisy than Y3in all four cases. Moreover, the converse proof for the second set of capacity results require both the Nair-Wang information inequality and the Csiszar sum lemma.

Multiple groupcasting over the broadcast channel (BC) is studied in a special setting. In particular, an inner bound is obtained for the K-receiver discrete memoryless (DM) BC for the diamond message set that consists of four groupcast messages: one desired by all receivers, one by all but two receivers, and two more desired by all but each one of those two receivers. The inner bound is based on rate-splitting and superposition coding and is given in explicit form herein as a union over coding distributions of four-dimensional poly-topes. When specialized to the so-called combination network, which is a class of three-layer (two-hop) broadcast networks parameterized by 2K-1 finite-and-arbitrary-capacity noiseless links from the source node in the first layer to as many nodes of the second layer, our top-down approach from the DM BC to the combination network yields an explicit inner bound as a single polytope via the identification of a single coding distribution. This inner bound consists of inequalities which, in a problem that is akin to finding a few needles in a haystack, are then identified to be within the class of a plethora of (indeed, infinitely many) generalized cut-set outer bounds recently obtained by Salimi et al for broadcast networks. We hence establish the capacity region of the general K-user combination network for the diamond message set, and do so in explicit form. Such a result implies a certain strength of our inner bound for the DM BC in that it (a) produces a hitherto unknown capacity region when specialized to the combination network and (b) may capture many, if not all, combinatorial aspects of the capacity region of the K-receiver DM BC itself (for the diamond message set).

The K-receiver discrete memoryless (DM) broadcast channel (BC) is considered in which each receiver is equipped with a cache memory of the same size. We obtain an upper bound on the capacity-memory tradeoff with uncoded pre-fetching, the highest rate of reliable communication for given cache size. This bound holds for the interleavable DM BC, a class of channels that subsumes the K-receiver degraded DM BC and the three-receiver less noisy DM BC. We then specialize our bound to the Gaussian BC, and show that it is tighter than that recently proposed in the literature for coded pre-fetching for a wide range of cache sizes as would be expected, but the two bounds coincide for sufficiently large cache size. In the two-receiver case, our bound is tight in that it is the exact capacity-memory trade-off with uncoded prefetching which implies that, in this case, coded prefetching does not enhance the capacity-memory tradeoff for sufficiently large cache size.

The K-user discrete memoryless (DM) broadcast channel (BC) with two nested multicast messages is studied in which one common message is to be multicast to all receivers and the second private message to a subset of receivers. The receivers that must decode both messages are referred to as private receivers and the others that must decode only the common message as common receivers. For two nested multicast messages, we establish the capacity region for several classes of partially ordered DM BCs characterized by the respective associated sets of pair-wise relationships between and among the common and private receivers, each described by the well-known pair-wise more capable or less noisy condition. For three classes of partially ordered DM BCs, the capacity region is shown to be simply achieved by two-level superposition coding and the proofs of the converses rely on a recently found information inequality. The rate region achievable by two-level superposition coding is then enhanced through a multi-level superposition coding scheme after splitting the private message into as many parts as there are common receivers and indirect decoding. A closed-form two-dimensional polyhedral (polygonal) description is obtained for it for a given coding distribution in spite of the indeterminate number of split rates via a structured form of Fourier-Motzkin elimination. Through a converse result that relies on the Csiszar sum lemma and that information inequality, a specialization of this region that corresponds to splitting the private message into just two sub-messages is proved to be the capacity region for several classes of partially ordered DM BCs beyond those for which two-level superposition coding is capacity optimal, thereby underscoring the benefit of rate-splitting. All previously known capacity results for partially ordered DM BCs with two nested multicast messages for the two and three-receiver DM BCs as well as DM BCs with one private or one common receiver are subsumed in the general results obtained in this work.

The two-receiver Gaussian broadcast channel (BC) is studied when each receiver has a cache memory. Using a joint cache-channel coding scheme, the exact capacity-memory tradeoff-the highest rate of reliable communication as a function of the cache size-is established for any cache size.

A K-receiver discrete memoryless (DM) broadcast channel (BC) with general message sets is studied. A general message set is one that contains any subset of or all possible 2K-1 groupcast messages, with each such message intended for a distinct subset of receivers. Message merging is a simple idea of bijectively mapping multiple messages into a single message, and hence with a rate that is the sum of the rates of the merged messages. Using a natural form of message merging it is shown that superposition coding of the merged messages and successive decoding of a subset of those messages at each receiver achieves the capacity region of the class of K-receiver interleavable DM BCs for any general message set. The interleavable class of DM BCs subsumes the K-receiver degraded DM BC and the less noisy DM BC in the three-receiver case as special cases. A generalization of that result is also given. For certain classes of message sets, message merging, superposition coding and successive decoding is shown to again achieve the capacity region, but for corresponding classes of channels that are larger than the interleavable DM BC. In each such class, there is a group of receivers that are not constrained to be ordered in strength by any notion of order (i.e., degraded, less noisy or more capable). Most known results on the optimality of superposition coding and successive decoding, including notably, for the interleavable DM BC with private messages, and for the recently found classes of DM BCs for two nested multicast messages with one private or one common receiver, are subsumed by the general -yet simply established -result of this paper.

In this paper, we consider the K-receiver discrete memoryless (DM) broadcast channel (BC) with K private messages of the same rate. Inspired by the decentralized caching problem which has received much interest of late, we consider the case where each message consists of 2Kindependent sub-messages, with each sub-message available at a distinct subset of receivers as side information. We assume that the rates of all the sub-messages available at the same number of receivers are the same. Hence, each receiver has exactly the same amount of information about each message, including its intended message, as side information. For this symmetric side information structure, we establish the symmetric capacity for the interleavable DM BC, a class of channels which subsumes the K-receiver degraded DM BC and the less noisy BC in the three-receiver case. Our coding scheme involves (a) network coding in the form of a bit-wise XOR of two or more messages (b) message merging where multiple messages are bijectively mapped into a single message with a rate that is the sum of the rates of the merged messages (c) superposition coding where the codebooks are generated for the merged messages and (d) successive decoding at each receiver to find its intended message with the aid of the side information.

Using an order-theoretic approach, a novel achievable rate region is obtained for the K-receiver discrete memoryless broadcast channel with two nested messages, one message desired by all receivers and the other desired by a subset of the receivers. When specialized to the combination network this inner bound is shown to achieve the capacity region when all but two receivers desire both messages.

The capacity region of the three-receiver discrete memoryless less noisy broadcast channel with message cognition is established in the case where the weakest receiver knows the message required by the strongest receiver prior to transmission. This problem was previously studied for the scalar Gaussian broadcast channel by Asadi et al but only inner and outer bounds were obtained. The capacity result of this paper can also be seen to augment the theory of the three-receiver discrete memoryless less noisy broadcast channel for which the capacity region was found previously by Nair and Wang but without message cognition.

The K-user discrete memoryless (DM) broadcast channel (BC) with two degraded messages, with one common message to be decoded by all receivers and a private message by a subset of receivers, is studied. The receivers that must decode both messages are referred to as private receivers and the remaining ones that need only decode the common message as common receivers. We obtain two main results. The first one establishes the capacity region of two classes of DM BCs characterized by the associated sets of pair-wise relationships between and among the common and private receivers, each described by the well-known more capable and less noisy conditions. For both these classes, the capacity region is achieved by superposition coding and joint decoding so that the main contribution herein lies in the proofs of the converses. When specialized to the two previously well-studied cases of a single private receiver and a single common receiver, the two aforementioned classes are respectively as large as or larger than those for which capacity was previously obtained. The second main result is a new inner bound in closed form that involves rate splitting, superposition coding, and indirect decoding and we state its capacity optimality for a new class of four-receiver DM BCs.

We consider a cognitive radio network with one primary (PU), one secondary user (SU), and two distinct destinations. SU not only exploits the idle time slots (i.e. PU is not transmitting) to send its own packets, but also interfere with the PU with a certain probability that is optimized to maximize the stable throughput of the SU under a delay constraint for the PU. This optimization problem is formulated using two schemes. First, the hard delay guarantee scheme where the objective is to maximize the throughput of the SU subject to the delay of the PU's packet is less than a certain value. Second, the soft delay guarantee scheme where the objective is to minimize the delay of the PU's packets minus a constant multiplied by the throughput of the SU. Numerical results reveal that none of the proposed outperforms the other in general. The first scheme ensures a fix delay performance for the PU's packets on the boundary of the stability region. While the second scheme guarantees a finite delay performance with higher stable throughput than that of the first scheme.

We consider a cooperative relaying system with any number of source terminals, one shared relay, and a common destination. We assume a slotted time division multiple access (TDMA) framework in which each source terminal is allocated a fraction of the time. We propose a novel hybrid cooperative scheme for the described network. In contrast to former works which assume that the relay only transmits in the idle time slots, we assume that the relay can, simultaneously, transmit with the source terminals via multi-access channel (MAC). In hybrid cooperative scheme, the relay operates in two modes each with a certain probability; the TDMA mode and the MAC mode. We derive expressions for the stability conditions and the average delay for all the queues in the network. We design the probability of each relaying mode such that the stable throughput is maximized while the network queues are stable. The problem is formulated as a non-convex quadratic constrained quadratic programming (QCQP) optimization problem. Numerical results reveal that the hybrid cooperative scheme significantly enhances the performance of the network in terms of stability region, average delay, and spectral efficiency.

We consider a cognitive radio system that consists of primary user, secondary user, and their destinations. The secondary user has a relaying capability, i.e., it transmits the relayed packets from the primary user. Unlike most of the previous works that restrict the secondary user to transmit only in the idle time slots, we assume that the secondary user interferes on the primary user with certain probability that is optimized to maximize the stable throughput of the secondary network under certain level of quality of service constraints for the primary one. We show how significantly our proposed scheme improves the performance of the secondary user and increases the maximum stable throughput of the primary user over the traditional cooperative policies that restrict the secondary user to exploit only the periods of silence of the primary user.