We consider a broadcast channel with three receivers and three-degraded message sets, i.e., the transmitter has a common message intended for all three receivers, a message intended for receivers 2 and 3, and a private message intended only for receiver 3. The messages are transmitted over a family of parallel degraded broadcast channels. In the most general case, the broadcast channel consists of the product of six parallel degraded broadcast channels, each with a different order of degradedness. We first consider an achievable rate region of Nair and El Gamal, by appropriately choosing independent input random variables and auxiliary random variables for each subchannel. We then show that the achievable rate region attains the capacity region for two different classes of such broadcast channels, one consisting of the product of five parallel degraded broadcast channels and another consisting of the product of three parallel degraded broadcast channels. To accomplish this, we make use of an information-theoretic inequality that may be proven using the Csiszár-sum identity. Next, we extend the result to the Gaussian case. We consider the aligned Gaussian MIMO broadcast channel consisting of the product of six parallel degraded Gaussian broadcast channels, where the Gaussian noise vectors for each of the users in each of the subchannels follow a degradedness order, i.e., the noise covariance matrices may be ordered in a positive semi-definite sense. We show that the Nair-El Gamal achievable rate region considered in this paper is maximized by Gaussian inputs. To prove that Gaussian inputs are optimal, we prove an extremal entropy inequality employing a new method recently introduced by Geng and Nair to prove the capacity region of the two-user Gaussian MIMO broadcast channel with common and private messages.

We consider the Wyner-Ziv and two way source coding problems with the erasure distortion measure. We characterize the rate-distortion regions for these settings, when the source and side information satisfy a positivity condition. Using our results, we show that, contrary to recent conjectures in the literature, feedback from the decoder to the encoder does not reduce the overall rate required in the Wyner-Ziv setting with erasure distortion, when the positivity condition is satisfied. Finally, we extend our techniques to characterize the rate-distortion regions of two multiterminal source coding settings, the Heegard-Berger setting, and the cascade source coding setting, when the positivity condition is satisfied.

In this paper, the sum-rate of a cognitive multiple access channel (C-MAC) is studied, where a secondary network (SN) with multiple secondary users (SUs) transmitting to a secondary base station (SBS) shares the spectrum band with a primary user (PU). An interference power constraint (IPC) is imposed on the SN to protect the PU. Under the IPC and the individual transmit power constraint (TPC) imposed on each SU, we investigate the power allocation strategies to maximize the sum-rate of the C-MAC without successive interference cancellation (SIC). We prove that the optimal solution must be at the extreme points of the feasible region. We show that Dynamic Time Division Multiple Access (D-TDMA) is optimal with high probability when the number of SUs is large. Furthermore, we show through simulations that the optimal power allocation to maximize the sum-rate of the C-MAC with SIC is optimal or near-optimal for our setting when D-TDMA is not optimal.

We consider the Wyner-Ziv and two way source coding problems with the erasure distortion measure. We characterize the rate-distortion regions for these settings when the source and side information satisfy a positivity condition. Using our results, we show that, contrary to recent conjectures in the literature, feedback from the decoder to the encoder does not reduce the overall rate required in the Wyner-Ziv setting with erasure distortion, when the positivity condition is satisfied. Finally, we extend our techniques to characterize the rate-distortion region of a Cascade source coding setting when the positivity condition is satisfied.

The compound broadcast channel models the situation where each receiver has a number of possible realizations and its message is to be decoded regardless of the actual realization. Weingarten et al. established the capacity region for the two-user degraded case where the realizations exhibit a degradedness order defined through a fictitious receiver. In this paper, we consider a K-receiver degraded compound broadcast channel where, instead of specifying fictitious receivers, the receivers exhibit a pair-wise degradedness order, i.e., each realization from a weaker receiver is stochastically degraded with respect to each realization from a stronger receiver. There is a restriction on the number of possible realizations for all the receivers to two. We first prove the capacity region for this discrete memoryless class of broadcast channels. The achievability follows readily from superposition coding and successive decoding. To facilitate the proof of the converse, we give an alternative characterization of the achievable rate region. The main contribution in this paper is to bypass the use of the Csiszέr-sum lemma in order to prove the converse for an arbitrary number of receivers. We also make use of our converse proof as well as Geng and Nair's technique to prove an extremal entropy inequality. This is then finally used to prove the capacity region of the equivalent class of Kreceiver aligned Gaussian MIMO degraded compound broadcast channels.

Nair and El Gamal established the capacity region of the three-receiver multilevel broadcast channel (MBC) with two-degraded message sets. For the three-receiver MBC with two-degraded message sets, the output at receiver 2 is a degraded version of the output at receiver 1. However, no order of degradedness is imposed on the output at receiver 3. The transmitter sends a common message to all three receivers and a private message to receiver 1. By considering a specific discrete-memoryless example, Nair and El Gamal showed that a direct extension of the Körner-Marton region (for the general two-receiver broadcast channel with degraded message sets) is strictly suboptimal. They also considered a three-receiver Gaussian product MBC and showed that, restricted to Gaussian inputs, the direct extension of the Körner-Marton region is again strictly suboptimal. However, whether Gaussian inputs are optimal remained unresolved. In this paper, we show that Gaussian inputs, along with time-sharing between rate points obtained with Gaussian inputs, achieve the capacity region of the three-receiver Gaussian multiple-input multiple-output MBC (this includes the three-receiver Gaussian product MBC considered by Nair and El Gamal) with two-degraded message sets. Our proof relies on the channel enhancement technique introduced by Weingarten as well as the perturbation approach employed by Liu and Viswanath.

The two-user compound Gaussian MIMO broadcast channel models the situation where each user has a finite set of possible realizations. The transmitter sends two messages, one for each user, such that each user must be able to decode its message regardless of the actual realization. This channel also models a broadcast channel (BC) with two groups of users and two messages, with one message intended for each group of users. Weingarten et al. established the capacity region for the degraded case where the realizations/users exhibit a degradedness order. The degradedness order is defined through an additional realization/user where the realizations/users from one set are degraded with respect to him and where he is degraded with respect to the realizations/users from the other set. To show that Gaussian inputs attain the capacity region, they proved a new extremal inequality and employed the use of the channel enhancement technique as well. In this paper, we extend the result to the N-user degraded compound Gaussian MIMO BC, where the N users exhibit a degradedness order similar to the two-user case. We first prove a generalization of the extremal inequality considered by Weingarten et al.; instead of considering the difference between the weighted sum of two sets of conditional differential entropies, we consider the summation of N - 1 sets of such differences, where the conditioning random variables of the N - 1 sets form a Markov chain. Our proof relies on the Gaussian perturbation approach, the necessary KKT conditions as well as a data processing inequality. Finally, we specialize the generalized extremal inequality to characterize the capacity region of the N-user degraded compound Gaussian MIMO BC. By making appropriate use of the necessary KKT conditions, we are able to do away with the use of the channel enhancement technique that was employed in the proof of the capacity region of the two-user case.

WiFi offloading is regarded as one of the most promising techniques for dealing with the explosive data increase in cellular networks due to its high data transmission rate and low requirement on devices. In this paper, we investigate the mobile data offloading problem through a third-party WiFi access point (AP) for a cellular mobile system. From the cellular operator's perspective, by assuming a usage-based charging model, we formulate the problem as a utility maximization problem. In particular, we consider three scenarios: 1) successive interference cancellation (SIC) available at both the base station (BS) and the AP; 2) SIC available at neither the BS nor the AP; and 3) SIC available at only the BS. For scenario 1, we show that the utility maximization problem can be solved by considering its relaxation problem, and the proposed data offloading scheme is near-optimal when the number of users is large. For scenario 2, we prove that with high probability the optimal solution is One-One-Association, i.e., one user connects to the BS and one user connects to the AP. For scenario 3, we show that with high probability there is at most one user connecting to the AP, and all the other users connect to the BS. By comparing these three scenarios, we prove that SIC decoders help the cellular operator maximize its utility. To relieve the computational burden of the BS, we propose a threshold-based distributed data offloading scheme. We show that the proposed distributed scheme performs well if the threshold is properly chosen.

Liu et al. proved an extremal entropy inequality using a vector generalization of the Costa entropy-power inequality (EPI). The generalized Costa EPI was proved, in turn, using a perturbation approach via a fundamental relationship between the derivative of mutual information and the minimum mean-square error (MMSE) estimate in linear vector Gaussian channels. In this paper, we consider two new variations of the (Liu et al.) extremal entropy inequality. Instead of employing perturbation approaches, we employ a new method recently introduced by Geng and Nair, which was used to resolve the capacity region of the Gaussian MIMO broadcast channel (BC) with common and private messages. As an application, we use one of the extremal entropy inequalities to prove the capacity region of a class of reversely degraded Gaussian MIMO BC with three users and three-degraded message sets.

Weingarten et al. established the capacity region for the two-user degraded compound broadcast channel where the realizations of each user exhibit a certain degradedness order. The degradedness order is defined through an additional fictitious user whose channel is stochastically degraded with respect to each realization from one set (the stronger receiver) while each realization from the other set (the weaker receiver) is stochastically degraded with respect to him. Rather than specifying a fictitious user, we consider a two-user degraded compound broadcast channel which is pair-wise degraded, i.e., each realization from the weaker receiver is stochastically degraded with respect to each realization from the stronger receiver. In this paper, we first prove the capacity region for a discrete memoryless class of this broadcast channels where the weaker receiver has only two possible realizations while there is an arbitrary number of possible realizations for the stronger receiver. Next, we consider the equivalent class of degraded compound MIMO Gaussian broadcast channels. To show that Gaussian inputs attain the capacity region, we prove a new extremal entropy inequality using a technique recently introduced by Geng and Nair that was used to resolve the capacity region of the two-user MIMO Gaussian broadcast channel with common and private information.

We consider a two-user broadcast channel (BC) with two-degraded message sets where a common message M2is intended for both receivers and a private message M1is intended for receiver one. There is an eavesdropper whose channel is stochastically degraded with respect to both receivers and both messages must be kept confidential from the eavesdropper. However, we do not assume any form of degradedness between the two receivers. We first characterize the capacity region of this class of discrete memoryless BC. Next, we consider the two-user Gaussian MIMO BC with two-degraded message sets and an eavesdropper. We characterize the capacity region for the case where the eavesdropper is only required to be stochastically degraded with respect to receiver one. We make use of the channel enhancement technique as well as an extremal entropy inequality of Liu et al. that was derived using the generalized Costa's entropy power inequality (EPI).

In this paper, we derive explicit expressions for the capacity region of the two-user symbol-asynchronous Gaussian vector multiple-access channel. Verdú considered the case where each user linearly modulates a fixed waveform in each symbol period, where the symbol periods for the users are not perfectly aligned at the receiver. He derived explicit capacity region expressions for the case where the transmitters have knowledge of the mutual offset and also for the case where the transmitters have no knowledge of the mutual offset. In this paper, we extend Verdú's results to allow each user to linearly modulate a set of orthonormal waveforms, instead of a single waveform, in each symbol period and with no restrictions imposed on the waveforms. We consider group power constraints, which include individual sum power constraints, as orthonormal waveforms assigned to each user may come from different frequency bands with different power constraints. Similar to the case where each user is allowed to linearly modulate only a single waveform, our results hold regardless of whether or not the transmitters are frame synchronous. In addition, we present some results that are necessary to numerically compute the capacity region expressions with general purpose convex optimization algorithms. Next, we simplify the capacity region expression when there are only individual sum power constraints and when the transmitters know the mutual offset. We also prove a sufficient condition for a similar simplification to hold when the transmitters have no knowledge of the mutual offset. Finally, we consider a specialized algorithm to numerically compute the simplified capacity region expression when the transmitters know the mutual offset.

We consider a broadcast channel with three receivers and three-degraded message sets, where the transmitter has a common message intended for all three receivers, a message intended for receivers 2 and 3, and a private message intended for receiver 3. The messages are transmitted over a family of parallel degraded broadcast channels. In the most general case, there are six parallel degraded broadcast channels with different orders of degradedness. We determine the capacity region for two classes of broadcast channels, one with five parallel degraded broadcast channels and the other with three parallel degraded broadcast channels. The main difficulty is in identifying the relevant auxiliary random variables in the proofs of the converse. To accomplish this, we make use of an information theoretic inequality that can be proven using the Csiszár-sum identity.

Weingarten et al. characterized the capacity region of a two-user compound MIMO broadcast channel when the two users exhibit a certain degradedness order. To show that Gaussian inputs attain the capacity region, they proved a new extremal inequality and made use of the channel enhancement technique. In this paper, we prove a generalization of the extremal inequality considered by Weingarten et al. We then apply the generalized extremal inequality to characterize the capacity region of the N-user compound MIMO Gaussian broadcast channel when the N users exhibit a degradedness order similar to the two-user case.

In this paper, we establish the capacity region of a new class of deterministic K-receiver broadcast channels with degraded message sets, where the output Yi, i ∈ {1, ..., K}, is a deterministic function of the channel input X and user i requires messages (M1, ... Mi). In this class of deterministic broadcast channels, the outputs Y1→ Y2→ Y3... → YKform a Markov chain for a sufficient class of input probability distributions p (x) ∈ P. The main idea of the coding strategy is to allow user i to decode not only its own messages (M1, ..., Mi), but also part of the messages (Mi+1, ..., MK) intended for user j ∈ {i + 1, i + 2, ..., K}. We then show that the achievable rate region attains the capacity region of this new class of deterministic K-receiver broadcast channels.

In this paper, we present results on the equivalence of some coding strategies for the general relay channel. Cover & El Gamal described two basic coding strategies for the relay channel, more commonly known as decode-and-forward and compress-and-forward. These two strategies were combined in a mixed strategy that employed irregular encoding and successive forward decoding to give a tighter lower bound for the capacity of the general relay channel. Recently, the authors presented two different mixed strategies, SeqBack decoding and SimBack decoding, that make use of regular encoding and backward decoding. We identify a termination problem in SeqBack/SimBack decoding and present a simple fix. Next, we compare the rates achievable with the various mixed strategies. We first show that SeqBack decoding and SimBack decoding achieve the same rate. We then present alternative characterizations, without feasibility constraints, for the rates achievable with the various mixed strategies. Comparing the alternative characterizations, we note that the rate of SeqBack/SimBack decoding contains the rate of Cover & El Gamal's mixed strategy since there is a more relaxed inequality in the rate expression. We also prove that simultaneously decoding all unknown quantities in each block at the receiver does not increase the achievable rate for backward decoding. Hence, successive decoding in each block proves to be just as effective as simultaneous decoding. Finally, we present a sliding-window decoding strategy that achieves the same rate as SeqBack/SimBack decoding. The sliding-window decoding strategy also avoids the aforementioned termination problem as the receiver commences decoding after three block decoding delay.

The relay channel consists of a transmitter inputx1, a relay inputx2, a relay outputy2, and a receiver outputy3. In this paper, we establish the capacity of three new classes of semi-deterministic relay channels: 1) a class of degraded semi-deterministic relay channels, 2) a class of semi-deterministic orthogonal relay channels, and 3) a class of semi-deterministic relay channels with relay-transmitter feedback. For the first class of relay channels, the output of the relayy2depends on a deterministic function of the transmitter's inputx1, i.e., ons=f1(x1), rather than onx1directly. In addition, the relay channels satisfy the condition thatS→ (X2,Y2) →Y3forms a Markov chain for all input probability distributionsp(x1,x2). Hence, the first class of relay channels includes, but is strictly not limited to, the class of degraded relay channels previously considered by Cover and El Gamal. The partial decode-and-forward strategy achieves the capacity of the class of degraded semi-deterministic relay channels. Next, we consider the class of semi-deterministic orthogonal relay channels where there are orthogonal channels from the relay to the receiver and from the transmitter to the receiver. In addition, the output of the relayy2is a deterministic function ofx1,x2andy3, i.e.,y2=f4(x1,x2,y3). The class of semi-deterministic orthogonal relay channels is a generalization of the class of deterministic relay channels considered by Kim. The compress-and-forward strategy achieves the capacity of the class of semi-deterministic orthogonal relay channels. For the third class of relay channels, there is a causal and noiseless feedback from the relay to the transmitter. In addition, similar to the second class of relay channels, the output of the relayy2is a deterministic function ofx1,x2, andy3. Both the generalized strategy of Gabbai and Bross and the hash-and-forward strategy of Kim achieve the capacity of the class of semi-deterministic relay channels with relay-transmitter feedback.

Verdu determined the capacity region of the symbol-asynchronous two-user Gaussian multiple-access channel. In this channel, each user modulates a fixed waveform in each symbol period and the symbol periods for the users do not coincide at the receiver. First, he explicitly evaluated the capacity region of this class of multiple-access channels in the case where the transmitters know the offset. The result was also extended to the case where the transmitters have no knowledge of the offset. In this paper, we extend the result to the case where each user modulates K orthogonal waveforms and the transmitters know the offset. In addition, the users' orthogonal waveforms are not assumed to be identical. Similar to the case where each user is allowed to modulate a fixed waveform, the result holds regardless of whether or not the transmitters are frame-asynchronous. We later extend the result to certain situations where the transmitters do not know the offset.

The capacity region of a class of discrete memoryless interference channels with common information is established. The setup is similar to the class of deterministic interference channels without common information studied by El Gamal and Costa, which was later extended to the class of deterministic interference channels with common information. In this paper, certain conditions that were originally imposed by El Gamal and Costa are relaxed and it is shown, by a specific example, that this new class of interference channels is strictly larger than the class of deterministic interference channels previously studied. In fact, the result of this paper is obtained by combining the class of deterministic interference channels with the class of discrete memoryless interference channels with strong interference. Hence, it also includes the capacity region of the class of discrete memoryless interference channels with strong interference as a special case.

The capacity regions of two new classes of deterministic relay channels are established. In the first class of deterministic relay channels, the family of conditional probability distributions describing the relay channel can be written as p(y2, y3|x1, x2)=p(y3|x1, x2)p(y2|s, x2, y3) where s is a deterministic function of x1, i.e., s=f1(x1). In addition, we require that Srarr(X2, Y2)rarrY3form a Markov chain for all input probability distributions p(x1, x2). In the second class of deterministic relay channels, there is causal noiseless feedback from relay to sender and the relay output is a deterministic function of x1, x2, and y3, i.e., y2=f3(x2, x2, y3). We consider two alternative schemes to achieve the capacity. The first is based on a generalized strategy of Gabbai and Bross. The second strategy is based on a ldquohash-and-forwardrdquo scheme by Cover and Kim.

In this correspondence, we derive a simplified description of the Han–Kobayashi rate region for the general interference channel. Using this result, we establish that the recently discovered Chong–Motani–Garg rate region is a new representation of the Han–Kobayashi region. Moreover, a tighter bound for the cardinality of the time-sharing auxiliary random variable emerges from our simplified description.

The capacity region of a class of discrete memoryless interference channels is established. The setup is similar to the class of deterministic interference channels studied by El Gamal and Costa. However, we relax certain conditions that were imposed by El Gamal and Costa. The capacity region of this class of interference channels also includes the capacity region of the discrete memoryless interference channels with strong interference. Finally, we extend the result to the case where both transmitters have a common message to transmit.

This correspondence studies coding strategies for a three-node relay channel. We start with the basic coding strategies of Cover and El Gamal: the relay decodes the source message and forward it to the destination (cooperation); the relay transmits its compressed channel outputs to the destination (facilitation); or the relay superimposes both cooperation and facilitation (generalized). In this paper, two new generalized strategies superimposing cooperation and facilitation are introduced and investigated on the general relay channel. The first strategy makes use of sequential backward (SeqBack) decoding while the second strategy makes use of simultaneous backward (SimBack) decoding. The achievable rate for the second strategy is shown to include that of the generalized strategy of Cover and El Gamal. Assuming zero-mean, jointly Gaussian random variables, the two new strategies give higher achievable rates than the generalized strategy of Cover and El Gamal for certain parameters on the Gaussian relay channel

We consider the two-user Z channel (ZC), where there are two senders and two receivers. One of the senders transmits information to its intended receiver (without interfering with the unintended receiver), while the other sender transmits information to both receivers. The complete characterization of the discrete memoryless ZC remains unknown to date. For the Gaussian ZC, the capacity has only been established for a crossover link gain of $1$. In this work, we study both the discrete memoryless ZC and the Gaussian ZC. We first establish achievable rates for the general discrete memoryless ZC. The coding strategy uses rate-splitting and superposition coding at the sender with information for both receivers. At the receivers, we use joint decoding. We then specialize the rates obtained to two different types of degraded discrete memoryless ZCs and also derive respective outer bounds to their capacity regions. We show that as long as a certain condition is satisfied, the achievable rate region is the capacity region for one type of degraded discrete memoryless ZC. The results are then extended to the two-user Gaussian ZC with different crossover link gains. We determine an outer bound to the capacity region of the Gaussian ZC with strong crossover link gain and establish the capacity region for moderately strong crossover link gain.

We consider the two-user Gaussian zigzag channel, where there are two senders and two receivers. One of the senders transmits information to its intended receiver (without interfering with the unintended receiver) while the other sender transmits information to both receivers. We first establish achievable rates for the discrete memoryless zigzag channel under strong interference which can be extended to the Gaussian zigzag channel with strong and very strong crossover link gain (a2ges 1). We also determine an outer bound for the Gaussian zigzag channel under strong and very strong crossover link gain (a2ges 1). Moreover, we establish the capacity of the Gaussian zigzag channel under (strictly) strong crossover link gain (1 les a2les 1 + P1)

This paper studies coding strategies for a three-node relay channel. We first review the basic coding strategies of Cover and El Gamal for the relay channel. Next, two new coding strategies superimposing cooperation and facilitation are developed. One of the coding strategies is shown to include the generalized strategy of Cover and El Gamal. For certain parameters of the Gaussian relay channel, the two new strategies give higher achievable rates than the generalized strategy of Cover and El Gamal