Achievable Rate Region Research Articles

Completely Uncoupled Algorithms for Network Utility Maximization

In this paper, we present two completely uncoupled algorithms for utility maximization. In the first part, we present an algorithm that can be applied for general non-concave utilities. We show that this algorithm induces a perturbed (by $\epsilon$) Markov chain, whose stochastically stable states are the set of actions that maximize the sum utility. In the second part, we present an approximate sub-gradient algorithm for concave utilities which is considerably faster and requires lesser memory. We study the performance of the sub-gradient algorithm for decreasing and fixed step sizes. We show that, for decreasing step sizes, the Cesaro averages of the utilities converges to a neighbourhood of the optimal sum utility. For constant step size, we show that the time average utility converges to a neighbourhood of the optimal sum utility. Our main contribution is the expansion of the achievable rate region, which has been not considered in the prior literature on completely uncoupled algorithms for utility maximization. This expansion aids in allocating a fair share of resources to the nodes which is important in applications like channel selection, user association and power control.

On the Evaluation of Marton’s Inner Bound for Two-Receiver Broadcast Channels

Marton’s inner bound is the best known achievable rate region for a general two-receiver discrete memoryless broadcast channel. In this paper, we establish improved bounds on the cardinalities of the auxiliary random variables appearing in this inner bound to the true rate region. We combine a perturbation technique, along with a representation using concave envelopes of information-theoretic functions that involve the use of auxiliary random variables, to achieve this improvement. The new cardinality bounds lead to a proof that a randomized-time-division strategy achieves every rate triple in Marton’s region for binary input broadcast channels. This extends the result by Hajek and Pursley which showed that the Cover-van der Muelen region was exhausted by the randomized-time-division strategy.

Achievable Rate Region Bounds and Resource Allocation for Wireless Powered Two Way Relay Networks

This paper investigates the wireless powered two way relay network (WPTWRN), where two single-antenna users and one single-antenna relay firstly harvest energy from signals emitted by a multi-antenna power beacon (PB) and then two users exchange information with the help of the relay by using their harvested energies. In order to improve the energy transfer efficiency, energy beamforming at the PB is deployed. For such a network, to explore the performance limit of the presented WPTWRN, an optimization problem is formulated to obtain the achievable rate region bounds by jointly optimizing the time allocation and energy beamforming design. As the optimization problem is non-convex, it is first transformed to be a convex problem by using variable substitutions and semidefinite relaxation (SDR) and then solve it efficiently. It is proved that the proposed method achieves the global optimum. Simulation results show that the achievable rate region of the presented WPTWRN architecture outperforms that of wireless powered one way relay network architecture. Results also show that the relay location has significant impact on achievable rate region of the WPTWRN.

On the Achievable Rate Region of NOMA Under Outage Probability Constraints

In this letter, we study the outage achievable rate region of non-orthogonal multiple access (NOMA), which is defined as the achievable rate region when all users are required to satisfy their outage probability constraints. First, we formally define the outage achievable rate region of NOMA assuming a slow fading channel model. Then, we introduce a successive interference cancelation (SIC) order under the assumption of statistical channel information. Under this assumption, we find that the outage capacity region of broadcast channel (BC) is also ϵ-achievable by NOMA, which requires the use of SIC, though the definition of outage in NOMA is different from that in BC. Combining the converse result, we get a full characterization of the outage achievable rate region of NOMA, which also shows the optimality of the SIC order used here. Then, we give some discussions about power allocation and the practical insights derived from the characterization. Finally, numerical simulations are provided.

Towards an Algebraic Network Information Theory: Simultaneous Joint Typicality Decoding

Consider a receiver in a multi-user network that wishes to decode several messages. Simultaneous joint typicality decoding is one of the most powerful techniques for determining the fundamental limits at which reliable decoding is possible. This technique has historically been used in conjunction with random i.i.d. codebooks to establish achievable rate regions for networks. Recently, it has been shown that, in certain scenarios, nested linear codebooks in conjunction with "single-user" or sequential decoding can yield better achievable rates. For instance, the compute-forward problem examines the scenario of recovering $L \le K$ linear combinations of transmitted codewords over a $K$-user multiple-access channel (MAC), and it is well established that linear codebooks can yield higher rates. Here, we develop bounds for simultaneous joint typicality decoding used in conjunction with nested linear codebooks, and apply them to obtain a larger achievable region for compute-forward over a $K$-user discrete memoryless MAC. The key technical challenge is that competing codeword tuples that are linearly dependent on the true codeword tuple introduce statistical dependencies, which requires careful partitioning of the associated error events.

Interference Channel With Full-Duplex Amplify-and-Forward Transmitter Cooperations

This paper considers a Gaussian interference channel (IC), where two transmitters send two messages to two receivers respectively. By utilizing the in-band full-duplex (FD) amplify-and-forward (AF) scheme, transmitter cooperations are deployed to enhance the system performance. In particular, each transmitter is capable of listening to its counterpart and then simultaneously transmits both the source signals to achieve higher power gain. Based on the proposed scheme, the equivalent channel model as well as the statistics of the accumulated residual self-interference and noise (ARIN) introduced by the transmitter cooperations and imperfect self-interference (SI) cancellation is analyzed. With the joint and single-user decoding schemes, the corresponding achievable rate regions are derived and a two-stage iterative algorithm is proposed to characterize these regions: in each step, fix the covariance matrix of the interferences and noises, and then adopt a two-step iterative semidefinite relaxation (SDR) method to optimize the two transmitters' transmission parameters, respectively. Simulation results reveal that the proposed scheme can significantly improve the achievable rate under several channel conditions.

Multiple Access Channels With Full-Duplex Amplify-and-Forward Transmitter Cooperations

In this paper, a full-duplex (FD) transmitter cooperative scheme is proposed to improve the achievable rate for multiple access channels (MACs). In the proposed scheme, by leveraging the FD amplify-and-forward (AF) protocol, two FD transmitters send their own signals and forward the received signals from their counterparts to the receiver, which adopts both the forward and backward decoding schemes to decode the source messages. First, the analyses of the equivalent channel model and the statistics of the accumulated additive white Gaussian noise and residual self-interference (ANRI) caused by imperfect self-interference cancellation are performed. Then, the achievable rate regions are obtained by utilizing both the forward and backward decoding schemes, and a two-stage iterative algorithm is proposed to characterize these regions: in each iteration, the covariance matrix of the ANRI is first updated; then, for the fixed covariance matrix of the ANRI, the transmission parameters of the two transmitters are calculated by a two-step iterative algorithm based on the parametric Dinkelbach algorithm, sequential convex programming (SCP), and semidefinite relaxation (SDR). The numerical results show that the proposed scheme outperforms the half-duplex cooperative scheme and conventional MAC scheme without cooperations when the channels between the two transmitters are in good condition.

Capacity and Achievable Rate Regions for Linear Network Coding Over Ring Alphabets

The rate of a network code is the ratio of the block size of the network’s messages to that of its edge codewords. We compare the linear capacities and achievable rate regions of networks using finite field alphabets to the more general cases of arbitrary ring and module alphabets. For non-commutative rings, two-sided linearity is allowed. Specifically, we prove the following for directed acyclic networks. First, the linear rate region and the linear capacity of any network over a finite field depend only on the characteristic of the field. Furthermore, any two fields with different characteristics yield different linear capacities for at least one network. Second, whenever the characteristic of a given finite field divides the size of a given finite ring, each network’s linear rate region over the ring is contained in its linear rate region over the field. Thus, any network’s linear capacity over a field is at least its linear capacity over any other ring of the same size. An analogous result also holds for linear network codes over module alphabets. Third, whenever the characteristic of a given finite field does not divide the size of a given finite ring, there is some network whose linear capacity over the ring is strictly greater than its linear capacity over the field. Thus, for any finite field, there always exist rings over which some networks have higher linear capacities than over the field.

Optical Mobile Communications: Principles, Implementation, and Performance Analysis

Owing to the rapid growth of mobile data communication and spectrum crunch at lower radio frequency, utilizing high frequency spectrum such as millimeter wave for ultra-high data rate mobile communications becomes necessary. Yet the propagation behaviors of high frequency radio waves make mobile communications rather challenging with a lot of technical problems, such as very large propagation loss. In this paper, we propose a novel approach, referred to as optical mobile communications (OMC), to cater to the need for high data rate mobile communication by exploiting optical beams. Taking spatial light modulator as an exemplary means of laser beam adaptation, we first present the system model of OMC. It is shown that the downlink channels in OMC are different from that in a system equipped with antennas emitting radio frequency signals. That is, the OMC channels for different mobile terminals are controllable to a large extent. This new feature creates a new dimension for performance optimization of OMC. We then investigate the achievable rate region of OMC using different multiple access schemes in a two-user downlink system. Numerical results show that expanded rate region can be achieved in OMC compared to the case where channels are not controllable, which shows the potential of OMC as a promising technique.

Plausible Deniability Over Broadcast Channels

In this paper, we introduce the notion of plausible deniability in an information theoretic framework. We consider a scenario where an entity that eavesdrops through a broadcast channel summons one of the parties in a communication protocol to reveal their message (or signal vector). It is desirable that the summoned party has enough freedom to produce a fake output that is likely plausible given the eavesdropper’s observation. We examine three variants of this problem—message deniability, transmitter deniability, and receiver deniability. In the first setting, the message sender is summoned to produce the sent message. Similarly, in the second and third settings, the transmitter and the receiver are required to produce the transmitted codeword and the received vector, respectively. For each of these settings, we examine the maximum communication rate that allows a given minimum rate of plausible fake outputs. First, for the message deniability problem, we fully characterize the capacity region for general broadcast channels. Next, for the transmitter deniability problem, we give an achievable region for general broadcast channels by fully characterizing the set of rate pairs’ achievable using deterministic coding schemes. Finally, for the receiver deniability problem, we give an achievable rate region for physically degraded broadcast channels.

Decentralized Caching Schemes and Performance Limits in Two-Layer Networks

We study the decentralized caching scheme in a two-layer network, which includes a server, multiple helpers, and multiple users. Basically, the proposed caching scheme consists of two phases, i.e., placement phase and delivery phase. In the placement phase, each helper/user randomly and independently selects contents from the server and stores them into its memory. In the delivery phase, the users request contents from the server, and the server satisfies each user through a helper. Different from the existing caching scheme, the proposed caching scheme takes into account the pre-stored contents at both helpers and users in the placement phase to design the delivery phase. Meanwhile, the proposed caching scheme exploits index coding in the delivery phase and leverages multicast opportunities, even when different users request distinct contents. Besides, we analytically characterize the performance limit of the proposed caching scheme, and show that the achievable rate region of the proposed caching scheme lies within constant margins to the information-theoretic optimum. In particular, the multiplicative and additive factors are carefully sharpened to be $\frac{1}{48}$ and 4, respectively, both of which are better than the state of arts. Finally, simulation results demonstrate the advantage of the proposed caching scheme compared with the state of arts.

An Achievable Region for the Cognitive Interference Relay Channel

In this paper, the causal cognitive interference relay channel (CCIRC) is considered. The CCIRC is obtained from the classic cognitive interference channel by introducing a full-duplex relay that has causal and noisy access to the transmitted signals and aids the communication between the two users. For this channel model, a simple upper bound on the capacity is initially established. Then, we derive an achievable rate region that jointly applies cooperative Han–Kobayashi rate splitting, block Markov encoding, superposition coding, Marton’s binning encoding, and backward decoding. In particular, these bounds are derived for both discrete memoryless model and Gaussian channel. Further, both our theoretical and numerical results indicate that the derived achievable rate region encompasses all known available results in the literature.

A Joint Typicality Approach to Compute–Forward

This paper presents a joint typicality framework for encoding and decoding nested linear codes in multi-user networks. This framework provides a new perspective on compute–forward within the context of discrete memoryless networks. In particular, it establishes an achievable rate region for computing a linear combination over a discrete memoryless multiple-access channel (MAC). When specialized to the Gaussian MAC, this rate region recovers and improves upon the lattice-based compute–forward rate region of Nazer and Gastpar, thus providing a unified approach for discrete memoryless and Gaussian networks. Furthermore, our framework provides some valuable insights on establishing the optimal decoding rate region for compute–forward by considering joint decoders, progressing beyond most previous works that consider successive cancellation decoding. Specifically, this paper establishes an achievable rate region for simultaneously decoding two linear combinations of nested linear codewords from $K$ senders.

Efficient quantum state transmission via perfect quantum network coding

Quantum network coding with the assistance of auxiliary resources can achieve perfect transmission of the quantum state. This paper suggests a novel perfect network coding scheme to efficiently solve the quantum $k$-pair problem, in which only a few assisting resources are introduced. Specifically, only one pair of maximally entangled state needs to be pre-shared between two intermediate nodes, and only $O(k)$ of classical information is transmitted though the network. Moreover, the classical communication used in our protocol does not cause transmission congestion, providing better adaptability to large-scale quantum $k$-pair networks.Through relevant analyses and comparisons, we demonstrate that our proposed scheme saves resources and has good application value, thereby showing its high efficiency. Furthermore, the proposed scheme achieves 1-max flow quantum communication, and the achievable rate region result is extended from its counterpart over the butterfly network.

Achievable Rate Region of the Buffer-Aided Two-Way Energy Harvesting Relay Network

In this paper, we investigate the buffer-aided two-way wireless energy harvesting (EH) relay network comprising two users and one relay, where two users exchange information with the help of the relay via three phases of EH, multiple-access, and broadcast . By transforming the opportunistic scheduling design problem into an equivalent convex problem, we present the adaptive design for the buffer-aided two-way EH relay network to maximize the long-term achievable rate region. To fulfill the delay sensitive transmission requirements, a delay-aware adaptive transmission (DAAT) scheduling scheme is proposed to guarantee the average end-to-end delivery delay by employing the Lyapunov optimization framework. Our analysis discloses that the average achievable rate region of the two-way wireless EH relay network can be improved when fully considering the potentials by deploying data buffer and energy storage at the relay. There exists an inherent tradeoff among the achievable sum rate, the delivery delay, and the power consumption. It is shown that, when a certain time delay is tolerable, the DAAT scheduling scheme is able to realize a rate region arbitrarily close to the achievable rate region of the buffer-aided two-way wireless EH relay network.

Applications of position-based coding to classical communication over quantum channels

Recently, a coding technique called position-based coding has been used to establish achievability statements for various kinds of classical communication protocols that use quantum channels. In the present paper, we apply this technique in the entanglement-assisted setting in order to establish lower bounds for error exponents, lower bounds on the second-order coding rate, and one-shot lower bounds. We also demonstrate that position-based coding can be a powerful tool for analyzing other communication settings. In particular, we reduce the quantum simultaneous decoding conjecture for entanglement-assisted or unassisted communication over a quantum multiple access channel to open questions in multiple quantum hypothesis testing. We then determine achievable rate regions for entanglement-assisted or unassisted classical communication over a quantum multiple-access channel, when using a particular quantum simultaneous decoder. The achievable rate regions given in this latter case are generally suboptimal, involving differences of Rényi-two entropies and conditional quantum entropies.

Partial feedback impact on achievable rate region in multiple‐access relay channels

SummaryFor discrete memoryless Slepian‐Wolf multiple‐access relay channel with relay‐sources feedback (SW‐MARC‐RSF), an achievable rate region via partial decode and forward strategy at the relay is proposed, and by extending the results to the continuous alphabet version, the corresponding achievable rate region of the Gaussian SW‐MARC‐RSF is obtained. It is shown that our results include the important previous works on multiple‐access channel (MAC) with feedback (Cover‐Leung rate region) and without feedback (Slepian‐Wolf [SW] rate region, etc) as special cases. Finally, through comparison of the achievable rate regions, with and without feedback, the impact of feedback on achievability is analyzed. The derived achievable rate region is shown to resolve the residual uncertainty at the receiver in an efficient way and demonstrates that in the partial decode and forward strategy, relay‐sources feedback increases the achievable rate region in both discrete memoryless and Gaussian multiple‐access relay channels.

Relay-Aided Secure Broadcasting for Visible Light Communications

A visible light communication broadcast channel is considered, in which a transmitter luminaire communicates with two legitimate receivers in the presence of an external eavesdropper. A number of trusted cooperative half-duplex relay luminaires are deployed to aid with securing the transmitted data. Transmitters are equipped with single light fixtures, containing multiple light emitting diodes, and receiving nodes are equipped with single photo-detectors, rendering the considered setting as a single-input single-output system. Transmission is amplitude-constrained to maintain operation within the light emitting diodes' dynamic range. Achievable secrecy rate regions are derived under such amplitude constraints for this multi-receiver wiretap channel, first for direct transmission without the relays, and then for multiple relaying schemes: cooperative jamming, decode-and-forward, and amplify-and-forward. Superposition coding with uniform signaling is used at the transmitter and the relays. Further, for each relaying scheme, secure beamforming vectors are carefully designed at the relay nodes in order to hurt the eavesdropper and/or benefit the legitimate receivers. Superiority of the proposed relaying schemes, with secure beamforming, is shown over direct transmission. It is also shown that the best relaying scheme depends on how far the eavesdropper is located from the transmitter and the relays, the number of relays, and their geometric layout.

Joint Base Station Clustering and Beamforming for Non-Orthogonal Multicast and Unicast Transmission With Backhaul Constraints

The demand for providing multicast services in cellular networks is continuously and fastly increasing. In this work, we propose a non-orthogonal transmission framework based on layered-division multiplexing (LDM) to support multicast and unicast services concurrently in cooperative multi-cell cellular networks with limited backhaul capacity. We adopt a two-layer LDM structure where the first layer is intended for multicast services, the second layer is for unicast services, and the two layers are superposed with different beamformers. Each user decodes the multicast message first, subtracts it, and then decodes its dedicated unicast message. We formulate a joint multicast and unicast beamforming problem with adaptive base station clustering that aims to maximize the weighted sum of the multicast rate and the unicast rate under per-BS power and backhaul constraints. To solve the problem, we first develop a branch-and-bound algorithm to find its global optimum. We then reformulate the problem as a sparse beamforming problem and propose a low-complexity algorithm based on convex-concave procedure. Simulation results demonstrate the significant superiority of the proposed LDM-based non-orthogonal scheme over orthogonal schemes in terms of the achievable multicast-unicast rate region.

Collective Secrecy Over the <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math> </inline-formula>-Transmitter Multiple Access Channel

This paper studies the problem of secure communication over a $K$ -transmitter multiple access channel (MAC) in the presence of an external eavesdropper, subject to a collective secrecy constraint (i.e., information leakage rate to an eavesdropper on a collection of messages that are from a pre-specified subset of the $K$ transmitters, say $\mathcal {S}\subseteq \mathcal {K}=\{1,2,\ldots, K\}$ , is made vanishing). Since secrecy is of concern only to transmitters $\{i|i\in \mathcal {S}\}$ but not to transmitters $\{i|i\in \mathcal {S}^{c}\}$ , where $\mathcal {S}^{c}=\mathcal {K}\backslash \mathcal {S}$ , different transmission strategies could be employed at transmitters $\{i|i\in \mathcal {S}^{c}\}$ . Consider the following two scenarios: 1) transmitters $\{i|i\in \mathcal {S}^{c}\}$ use deterministic encoders (which are conventionally used for MAC without secrecy), competing for the channel resource (i.e., being competitive) and 2) transmitters $\{i|i\in \mathcal {S}^{c}\}$ use stochastic encoders, helping to hide other transmitters’ messages from the eavesdropper (i.e., being cooperative). As a result, we establish the respective $\mathcal {S}$ -collective secrecy achievable rate regions and demonstrate the advantage of being cooperative theoretically and numerically. To this end, in addition to the standard techniques, our results build upon two techniques. The first is a generalization of Chia-El Gamal’s lemma on entropy bound for a set of codewords given partial information. The second is to utilize a compact representation of a list of sets that, together with submodular properties of mutual information functions involved, leads to an efficient Fourier-Motzkin elimination. These two approaches allow us to derive achievable regions in this work, and could also be of independent interest in other context.