Achievable Rate Region Research Articles

Optimal Scheduling for Emptying a Wireless Network: Solution Characterization, Applications, Including Deadline Constraints

Link scheduling, i.e., which links should transmit together and for how long, has been and remains a cornerstone optimization problem in wireless networking. In minimum-time scheduling, the task is to minimize the amount of time before emptying the data demand residing at the source nodes. We derive a complete structural characterization of the solution that unifies and significantly extends the known results. First, we approach link scheduling with a general system model without restrictions on the shape of the achievable rate region. Then, we give and prove a solution characterization of optimality that is conceptually simple yet powerful. We demonstrate several applications of this characterization for analysis of optimality and problem tractability. Next, we consider a significant extension by including deadline constraints, under which optimal scheduling becomes much more complex. Yet, we show how our formulation yields a solution description for that problem as well.

Achievable Rate Regions for Source Coding with Delayed Partial Side Information

In this paper, we consider a source coding with side information partially used at the decoder through a codeword. We assume that there exists a relative delay (or gap) of the correlation between the source sequence and side information. We also assume that the delay is unknown but the maximum of possible delays is known to two encoders and the decoder, where we allow the maximum of delays to be subject to change by the block length. In this source coding, we give an inner bound and an outer bound on the achievable rate region, where the achievable rate region is the set of rate pairs of encoders such that the decoding error probability vanishes as the block length tends to infinity. Furthermore, we clarify that the inner bound coincides with the outer bound when the maximum of delays for the block length converges to a constant.

Stringently Delay-Constrained Group Decoding and Adaptive Transmission for Multi-User Interference Channel

Low latency and high reliability are key features of the fifth-generation (5G) machine-type communications. In this paper, we provide a stringently delay-constrained model for multi-user interference channel, and formulate the rate and power allocation problem based on Markov decision process (MDP), which is solved by value iteration algorithm. In particular, to make timely transmission of each packet after being encoded, we characterize the delay constraint on sum of buffering delay and transmission delay. Then, the rate splitting and group decoding are employed at transmitters and receivers, respectively, which can offer significant improvement of achievable rate region. In addition, we also consider the receiving latency and propose novel delay-constrained partial group decoding (DC-CPGD), where all desired messages can be decoded within allowable interference cancellation steps to effectively control this latency. Two rate allocation algorithms are proposed with limited information exchange. Numerical results demonstrate that the proposed DC-CPGD can perform close to exhaustive search, and the proposed MDP-based adaptive transmission combined with DC-CPGD can significantly reduce the transmission cost under stringent delay requirement.

Buffer-Aided Adaptive Wireless Powered Communication Network With Finite Energy Storage and Data Buffer

In this paper, the access point (AP) in a wireless network is assumed to provide energy supply via wireless energy transfer to multiple terminals in the downlink, and all the terminals use the harvested energy to transmit their collected data to the AP in the uplink in a time division multiple access (TDMA) manner. Each terminal is provisioned with a finite energy storage and a finite data buffer to store the harvested energy and to buffer the arrived data traffic, respectively. Due to the limited data buffer and energy storage size, there might be data loss due to either data buffer overflow or energy storage depletion. Firstly, we aim at maximizing the long-term weighted sum-rate through energy beamforming vector design, power allocations, rate control, time allocations, and transmission mode selection subject to average transmit power, peak transmit power, data loss ratio requirements, practical data buffer as well as energy storage constraints. Secondly, the weighted max-min scheduling scheme is proposed to guarantee the fair access requirement by multiple terminals. Numerical analyses are presented to show that, the proposed adaptive design can substantially improve the average achievable rate region, while the proposed weighted max-min fair scheduling can effectively ensure the fair access requirements.

Outage Constrained Robust Beamforming for Sum Rate Maximization in Multi-Beam Satellite Systems

This letter investigates robust beamforming for multi-beam satellite communications in face of a phase error of channel state information. From the perspective of a practical system, we first formulate a sum rate maximization problem under the outage probability constraint of each user and the power consumption constraint of each individual feed. To handle the challenging problem, we characterize the Pareto frontier of the outage constrained achievable rate region based on a rate-profile method. In particular, a conservative approximation of the probabilistic constraint is achieved by means of the Taylor series expansion and the large deviation inequality. Numerical results validate the effectiveness and superiority of our proposed scheme compared to the existing approaches and give an insight into the impact of on-board payloads on robust beamforming.

Performance Analysis and Optimization of Cooperative Full-Duplex D2D Communication Underlaying Cellular Networks

This paper investigates the cooperative full-duplex device-to-device (D2D) communication underlaying a cellular network, where the cellular user (CU) acts as a full-duplex relay to assist the D2D communication. To simultaneously support D2D relaying and uplink transmission, superposition coding and successive interference cancellation are adopted at the CU and the D2D receiver, respectively. The achievable rate region and joint outage probability are derived to characterize the performance of the considered system. In consideration of the fairness between the cellular uplink and the D2D link, an optimal power allocation scheme is proposed to maximize the minimum achievable rate of them. Besides, by analyzing the upper bound of the joint outage probability, we study a suboptimal power allocation to improve the outage performance. The simulation results confirm the theoretical analysis and the advantages of the proposed power allocation schemes.

Broadcast Approach to Multiple Access With Local CSIT

A two-user multiple access channel is considered, in which the channels undergo slow block fading and the state of each channel is known only to its corresponding transmitter. This paper proposes a novel broadcast strategy for multiple access communication in this channel. In the broadcast approach, in principle, a transmitter with CSI uncertainty sends multiple independent superimposed information layers where the rate of each layer is adapted to a specific channel realization. In the existing broadcast approaches to multiuser communication, the transmitters often directly adopt a single-user strategy and each transmitter adapts its transmission to one unknown channel. The novel aspect of the proposed strategy is that it adapts the designed codebooks to the state of the entire network. This is motivated by the fact that the contribution of each user to the network-wide measures (e.g., capacity region) depends not only on the user’s direct channel to the receiver, but also on the qualities of other channels. Average achievable rate region and outer bounds on the capacity region are characterized. Furthermore, the expected capacity region is investigated, where most part of the capacity region boundary is characterized. Finally, an asymptotic capacity region is also characterized.

Improper Gaussian signaling scheme for the two‐users X‐interference channel

Different from conventional proper Gaussian signalling (PGS), whose achievable rate depends on the input signals' covariances only, the capacity of channels with improper Gaussian signalling (IGS) is a function with the signals' covariances and pseudo-covariances. Thus, the additional degree of freedom provided by pseudo-covariance is available to improve the achievable rate. In this study, the authors investigate the achievable rate region of two-users X-interference channel (IC) in the condition of applying IGS. By treating the interference as additive Gaussian noise, the authors analyze the mathematical expression of capacity based on Shannon's theorem. Specifically, for the two-users simple input, simple output (SISO)-IC, they propose two optimal signalling schemes to achieve the Pareto boundary in situations of employing PGS and IGS, respectively. In these optimal signalling schemes, the transparent geometric model which takes less computational complexity is applied to calculate the optimal transmission parameters for the Pareto boundary. Numerical simulation results show that the proposed IGS strategies can achieve larger achievable rate region and a greater sum rate. Finally, the authors give an in-depth discussion about the structure of the Pareto boundary, which is characterised by the degree of impropriety measured by the covariance and the pseudo-covariance of signals.

Generalized Compression Strategy for the Downlink Cloud Radio Access Network

This paper studies the downlink of a cloud radio access network (C-RAN) in which a centralized processor (CP) communicates with mobile users through base stations (BSs) that are connected to the CP via finite-capacity fronthaul links. Information theoretically, the downlink of a C-RAN is modeled as a two-hop broadcast-relay network. Among the various transmission and relaying strategies for such model, this paper focuses on the compression strategy, in which the CP centrally encodes the signals to be broadcast jointly by the BSs, then compresses and sends these signals to the BSs through the fronthaul links. We characterize an achievable rate region for a generalized compression strategy with Marton’s multicoding for broadcasting and multivariate compression for fronthaul transmission. We then compare this rate region with the distributed decode-forward (DDF) scheme, which achieves the capacity of the general relay networks to within a constant gap, and show that the difference lies in that DDF performs Marton’s multicoding and multivariate compression jointly as opposed to successively as in the compression strategy. A main result of this paper is that under the assumption that the fronthaul links are subject to a sum capacity constraint, this difference is immaterial; so, for the Gaussian network, the compression strategy based on successive encoding can already achieve the capacity region of the C-RAN to within a constant gap, where the gap is independent of the channel parameters and the power constraints at the BSs. As a further result, for C-RAN under individual fronthaul constraints, this paper also establishes that the compression strategy can achieve to within a constant gap to the sum capacity.

Quasi Structured Codes for Multi-Terminal Communications

A new class of structured codes called quasi group codes (QGCs) is introduced. A QGC is a subset of a group code. In contrast with the group codes, QGCs are not closed under group addition. The parameters of the QGC can be chosen, such that the size of $\mathcal {C}+\mathcal {C}$ is equal to any number between $|\mathcal {C}|$ and $|\mathcal {C}|^{2}$ . We analyze the performance of a specific class of QGCs. This class of QGCs is constructed by assigning single-letter distributions to the indices of the codewords in a group code. Then, the QGC is defined as the set of codewords whose index is in the typical set corresponding to these single-letter distributions. The asymptotic performance limits of this class of QGCs are characterized using single-letter information quantities. Corresponding covering and packing bounds are derived. It is shown that the point-to-point channel capacity and optimal rate-distortion function are achievable using QGCs. Coding strategies based on QGCs are introduced for three fundamental multi-terminal problems: the Korner-Marton problem for modulo prime-power sums, computation over the multiple access channel (MAC), and MAC with distributed states. For each problem, a single-letter achievable rate-region is derived. It is shown, through examples, that the coding strategies improve upon the previous strategies based on the unstructured codes, linear codes, and group codes.

Secure Relaying in Non-Orthogonal Multiple Access: Trusted and Untrusted Scenarios

A downlink single-input single-output non-orthogonal multiple access setting is considered, in which a base station (BS) is communicating with two legitimate users in two possible scenarios of unsecure environments: existence of an external eavesdropper and communicating through an untrusted relay. For the first scenario, a number of trusted cooperative half-duplex relays is employed to assist with the BS's transmission and secure its signals from the external eavesdropper. Various relaying schemes are proposed and analyzed for that matter: cooperative jamming, decode-and-forward, and amplify-and-forward. For each scheme, secure beamforming signals are devised at the relays to maximize the achievable secrecy rate regions. For the second scenario, with the untrusted relay, achievable secrecy rate regions are derived for two different relaying schemes: compress-and-forward and amplify-and-forward, under two different modes of operation. In the first mode, coined passive user mode, the users receive signals from both the BS and the untrusted relay, and combine them to decode their messages. In the second mode, coined active user mode, the users transmit a cooperative jamming signal simultaneously with the BS's transmission to further confuse the relay. Focusing on half-duplex nodes, the users cannot receive the BS's signal while jamming the relay, i.e., while being active, and rely only on the signals forwarded to them by the relay. It is shown that the best relaying scheme highly depends on the system parameters, in particular distances between the nodes, and also on which part of the secrecy rate region the system is to operate at.

Rate-storage regions for Extractable Source Coding with side information

This papers considers the coding of a source X with J decoders, each having access to a different side information Y(j). We define a new source coding problem called Extractable Source Coding with Side Information (ESC-SI). In this problem, the server stores one single coded description of the source, from which J descriptions can be extracted without re-encoding, depending on the side information available at the decoder. We want to minimize both the storage rate of the source on the server, and the J transmission rates from the server to the decoders. We provide the achievable storage-transmission rate regions for lossless source coding of general, non i.i.d., non-ergodic sources, and the achievable storage-transmission rate-distortion regions for lossy source coding for non i.i.d. Gaussian sources. The regions obtained for such general source models provide insightful design guidelines for practical applications.

Generalizing Multiple Access Wiretap and Wiretap II Channel Models: Achievable Rates and Cost of Strong Secrecy

In this paper, new two-user multiple access wiretap channel models are studied. First, the multiple access wiretap channel II with a discrete memoryless main channel under different wiretapping scenarios is introduced. The wiretapper, as in the classical wiretap channel II model, chooses a fixed-size subset of the channel uses, in which it obtains noise-free observations of one of the codewords: a deterministic function, e.g., superposition, of the two codewords or each of the two codewords. A fourth wiretapping scenario is considered, in which the wiretapper, in each position it chooses, decides to observe either one of the codewords or both codewords, with an overall budget on the number of its noiselessly observed symbols. These, thus, extend the recently examined wiretap channel II with a noisy main channel to a multiple access setting with a variety of attack models for the wiretapper. Next, the proposed multiple access wiretap channel II models are further generalized to the case when the wiretapper observes the outputs of a discrete memoryless channel, instead of erasures, outside the subset of noiseless observations. Achievable strong secrecy rate regions for all the proposed models are derived. Achievability is established by solving dual multi-terminal secret key agreement problems in the source model and converting the solution to the original channel models using probability distribution approximation arguments. The derived achievable rate regions quantify the secrecy cost due to the additional capabilities of the wiretapper with respect to the previous multiple access wiretap models.

On the capacity of the state‐dependent interference relay channel

SummaryThis paper considers the state‐dependent interference relay channel (SIRC) in which one of the two users may operate as a secondary user and the relay has a noncausal access to the signals from both users. For discrete memoryless SIRC, we first establish the achievable rate region by carefully merging Han‐Kobayashi rate splitting encoding technique, superposition encoding, and Gelfand‐Pinsker encoding technique. Then, based on the achievable rate region that we derive, the capacity of the SIRC is established in many different scenarios including (a) the weak interference regime, (b) the strong interference regime, and (c) the very strong interference regime. This means that our capacity results contain all available known results in the literature. Next, the achievable rate region and the associated capacity results are also evaluated in the case of additive Gaussian noise. Additionally, many numerical examples are investigated to show the value of our theoretical derivations.

Multiple access relay channel: Achievable rates over orthogonal channels

In this paper, we consider the multiple access relay channel (MARC) in which two users want to communicate with a destination in the presence of a common intermediate node, the relay. This paper considers the case in which the relay can partially listen to both the users until it can estimate their signals. Specifically, a two-phase transmission scheme, (i) listening phase, and (ii) forwarding phase, is designed toward deriving the achievable rate region. In particular, the achievable rate region is basically derived in the cases of additive Gaussian channel and Rayleigh fading channel. Our numerical results show that (i) the derived achievable rate region contains the available rate region in the literature, and (ii) the sum rate has a concave relation with the number of channel uses in the listening phase.

Capacity Region of the Symmetric Injective $K$ -User Deterministic Interference Channel

We characterize the capacity region of the symmetric injective $K$ -user deterministic interference channel for all channel parameters. The achievable rate region is derived by first projecting the achievable rate region of Han–Kobayashi (HK) scheme, which is in terms of common and private rates for each user, along the direction of aggregate rates for each user (i.e., the sum of common and private rates). We then show that the projected region is characterized by only the projection of those facets in the HK region for which the coefficient of common rate and private rate are the same for all users, hence simplifying the region. Furthermore, we derive a tight converse for each facet of the simplified achievable rate region.

Rate Region of the ZF Precoder in a $2\times2$ Multiuser Optical IM/DD Channel

We derive an achievable rate region (ARR) of the zero-forcing precoder in a 2 $\times $ 2 multi-user multiple-input single-output broadcast intensity-modulation/direct-detection channel. A per-light emitting diode (LED) peak optical power constraint along with a per-LED average optical power constraint with inequality (Type-I constraint) generally considered in optical wireless communication systems is imposed for which we analytically characterize the boundary of the proposed ARR. Then, we compare this ARR with that under a per-LED peak optical power constraint along with a per-LED average power constraint with equality (Type-II constraint), which is considered in visible light communication systems for constant illumination requirement. Our analysis reveals that when the ratio ( $\beta $ ) of the maximum allowed per-LED average optical transmit power to the per-LED peak power is less than or equal to half ( $\beta \leq 1/2$ ), the ARR under both the constraints is the same. However, Type-I constrained system is analytically shown to be more power efficient in terms of the required total average transmit optical power. When $\beta > 1/2$ , the ARR under the Type-I constraint remains constant with increasing $\beta $ , whereas the ARR under the Type-II constraint shrinks.

Cache-Aided Non-Orthogonal Multiple Access: The Two-User Case

In this paper, we propose a cache-aided non-orthogonal multiple access (NOMA) scheme for spectrally efficient downlink transmission. The proposed scheme not only reaps the benefits associated with NOMA and caching, but also exploits the data cached at the users for interference cancellation. As a consequence, caching can help to reduce the residual interference power, making multiple decoding orders at the users feasible. The resulting flexibility in decoding can be exploited for improved NOMA detection. We characterize the achievable rate region of cache-aided NOMA and derive the Pareto optimal rate tuples forming the boundary of the rate region. Moreover, we optimize cache-aided NOMA for minimization of the time required for completing file delivery. The optimal decoding order and the optimal transmit power and rate allocation are derived as functions of the cache status, the file sizes, and the channel conditions. Simulation results confirm that, compared to several baseline schemes, the proposed cache-aided NOMA scheme significantly expands the achievable rate region and increases the sum rate for downlink transmission, which translates into substantially reduced file delivery times.

On the Two-User MISO Interference Channel With Single-User Decoding: Impact of Imperfect CSIT and Channel Dimension Reduction

This paper examines the Rayleigh fading multiple-input single-output interference channel with single-user decoding and limited channel state information (CSI) feedback. Its contribution is twofold. First, the achievable rate-region with imperfect CSI at the transmitters due to channel quantization errors is analyzed for the two-user case. An analytically tractable inner bound on that region is derived, which provides insights into the problem. Similarly to the case of perfect CSI at the transmitters, it can be shown that beamforming constitutes an optimal strategy for achieving the boundary points of the inner bound. Second, we present a novel CSI feedback scheme that reduces the cross-link CSI feedback overhead, and enhances throughput for any rate-limited feedback scheme. This feedback reduction is crucial when control channels for sharing information between transmitters and unintended receivers are rate limited. A distinguishing feature of the proposed scheme is that feedback is taken into account already at the channel estimation stage. While maintaining a high array gain in the direct channel towards the intended user, the scheme induces an effective low-dimensional cross-link channel, which can be quantized more accurately than the full-dimensional channel. This eventually leads to enhanced performance while maintaining a low CSI feedback overhead. Finally, the proposed feedback scheme is extended to the case of $N>2$ users and shown to provide a significant reduction in CSI feedback overhead in a practically oriented setting.

Information Theoretic Security for Shannon Cipher System under Side-Channel Attacks †.

In this paper, we propose a new theoretical security model for Shannon cipher systems under side-channel attacks, where the adversary is not only allowed to collect ciphertexts by eavesdropping the public communication channel but is also allowed to collect the physical information leaked by the devices where the cipher system is implemented on, such as running time, power consumption, electromagnetic radiation, etc. Our model is very robust as it does not depend on the kind of physical information leaked by the devices. We also prove that in the case of one-time pad encryption, we can strengthen the secrecy/security of the cipher system by using an appropriate affine encoder. More precisely, we prove that for any distribution of the secret keys and any measurement device used for collecting the physical information, we can derive an achievable rate region for reliability and security such that if we compress the ciphertext using an affine encoder with a rate within the achievable rate region, then: (1) anyone with a secret key will be able to decrypt and decode the ciphertext correctly, but (2) any adversary who obtains the ciphertext and also the side physical information will not be able to obtain any information about the hidden source as long as the leaked physical information is encoded with a rate within the rate region. We derive our result by adapting the framework of the one helper source coding problem posed and investigated by Ahlswede and Körner (1975) and Wyner (1975). For reliability and security, we obtain our result by combining the result of Csizár (1982) on universal coding for a single source using linear codes and the exponential strong converse theorem of Oohama (2015) for the one helper source coding problem.