Achievable Rate Region Research Articles

Sum-Rate Maximization for Linearly Precoded Downlink Multiuser MISO Systems With Partial CSIT: A Rate-Splitting Approach

This paper considers the sum-rate (SR) maximization problem in downlink multi-user multiple input simgle output (MU-MISO) systems under imperfect channel state information at the transmitter (CSIT). Contrary to existing works, we consider a rather unorthodox transmission scheme. In particular, the message intended to one of the users is split into two parts: a common part which can be recovered by all users, and a private part recovered by the corresponding user. On the other hand, the rest of users receive their information through private messages. This rate-splitting (RS) approach was shown to boost the achievable degrees of freedom when CSIT errors decay with increased SNR. In this paper, the RS strategy is married with linear precoder design and optimization techniques to achieve a maximized ergodic SR (ESR) performance over the entire range of SNRs. Precoders are designed based on partial CSIT knowledge by solving a stochastic rate optimization problem using means of sample average approximation coupled with the weighted minimum mean square error approach. Numerical results show that in addition to the ESR gains, the benefits of RS also include relaxed CSIT quality requirements and enhanced achievable rate regions compared with conventional transmission with no rate-splitting.

Capacity and Rate Regions of a Class of Broadcast Interference Channels

In this paper, a class of broadcast interference channels (BIC) is investigated, where one of the two broadcast receivers is subject to interference coming from a point-to-point transmission. For a general discrete memoryless broadcast interference channel (DM-BIC), an achievable scheme based on message splitting, superposition, and binning is proposed and a concise representation of the corresponding achievable rate region $\mathcal {R}$ is obtained. Two partial-order broadcast conditions interference-oblivious less noisy and interference-cognizant less noisy are defined, thereby extending the usual less noisy condition for a regular broadcast channel by taking interference into account. Under these conditions, a reduced form of $\mathcal {R}$ is shown to be equivalent to a rate region based on a simpler scheme, where the broadcast transmitter uses only superposition. Furthermore, if interference is strong for the interference-oblivious less noisy DM-BIC, the capacity region is given by the aforementioned two equivalent rate regions. For the interference-cognizant less noisy DM-BIC, it is argued that the strong but not very strong interference condition does not exist, and in this case, the capacity region for the very strong interference is obtained. For a Gaussian broadcast interference channel, channel parameters are categorized into three regimes. For the first two regimes, which are closely related to the two partial-order broadcast conditions, achievable rate regions are derived by specializing the corresponding achievable schemes of DM-BICs with Gaussian input distributions. The entropy power inequality-based outer bounds are obtained by combining bounding techniques for a Gaussian broadcast channel and a Gaussian interference channel. These inner and outer bounds lead to either exact or approximate characterizations of capacity regions and sum capacity under various conditions. For the remaining complementing regime, inner and outer bounds are also provided.

A Lattice-Based Compress-and-Forward Strategy for Gaussian Two-Way Relay Channel With Direct Links

In this letter, the Gaussian two-way relay channel with direct links is investigated in which two users aim at exchanging their messages with the help of a relay node. We propose a new lattice-based compress-and-forward strategy and obtain its achievable rate-region. We show that the proposed scheme is superior to all previously known achievable schemes for channel gains larger than one. In particular, under the symmetric case, the proposed scheme is able to achieve a capacity region within 0.5 bit or $ {({1}/{2})\log 3\cong 0.79}$ bit, depending on the power of the relay.

Distributed Medium Access Over Time-Varying Channels

Recent studies on MAC scheduling have shown that carrier sense multiple access (CSMA) algorithms can be throughput optimal for arbitrary wireless network topology. However, these results are highly sensitive to the underlying assumption on ‘static’ or ‘fixed’ system conditions. For example, if channel conditions are time-varying, it is unclear how each node can adjust its CSMA parameters, so-called backoff and channel holding times, using its local channel information for the desired high performance. In this paper, we study ‘channel-aware’ CSMA (A-CSMA) algorithms in time-varying channels, where they adjust their parameters as some function of the current channel capacity. First, we assume that backoff rates can be arbitrary large and show that the achievable rate region of A-CSMA equals to the maximum rate region if and only if the function is exponential. Furthermore, given an exponential function in A-CSMA, we design updating rules for their parameters, which achieve throughput optimality for an arbitrary wireless network topology. They are the first CSMA algorithms in the literature which are proved to be throughput optimal under time-varying channels. Moreover, we also consider the case when back-off rates of A-CSMA are restricted compared to the speed of channel variations, and characterize the throughput performance of A-CSMA in terms of the underlying wireless network topology. Our results not only guide a high-performance design on MAC scheduling under highly time-varying scenarios, but also provide new insights on the performance of CSMA algorithms in relation to their backoff rates and underlying network topologies.

Short Message Noisy Network Coding With Sliding-Window Decoding for Half-Duplex Multihop Relay Networks

In this paper, we present a cooperative relaying strategy for half-duplex multihop relay networks. This scheme consists of three parts: 1) relay selection to yield a layered relay network; 2) group successive relaying that establishes a relay schedule to efficiently exploit half-duplex relays; and 3) a cooperative relaying scheme named short message noisy network coding with sliding-window decoding (SNNC-SW) that outperforms other state-of-the-art information theoretical schemes with lower decoding complexity and delay. We derive an achievable rate region of the proposed SNNC-SW scheme and attain a closed-form rate expression in the asymptotic case for several network models of interests. We then focus on the first part of our relaying strategy regarding efficient relay selection. We develop interference-harnessing routing that exploits the fact that in SNNC-SW, interference is treated as a useful signal. We show that, due to the efficient treatment of interference, this scheme can outperform routing schemes that deploy store-and-forward, a solution previously proposed for practical wireless multihop networks. Finally, we develop a low-complexity successive decoder of our scheme (implemented by a conventional MIMO decoder), which is a solution that can readily be implemented in practice. It is shown that also this practical scheme provides a significant gain over routing (based on store-and-forward) and the performance gap increases as the network becomes denser.

Two-Way Multiple Relays Channel: Achievable Rate Region and Optimal Resources

This paper considers a communication model containing two users that exchange their information with the help of multiple parallel relay nodes. To avoid interference at these common nodes, two users are required to transmit over the different frequency bands. Based on this scenario, the achievable rate region is initially derived. Next, an optimization scheme is described to choose the best relays that can be used by each user. Then, two power allocation optimization schemes are investigated to allocate the proper average power value to each node. Finally, comparisons between these two optimization schemes are carried out through some numerical examples.

On the Individual Secrecy Capacity Regions of the General, Degraded, and Gaussian Multi-Receiver Wiretap Broadcast Channel

In this paper, secure communication over a broadcast channel with multiple legitimate receivers and an external eavesdropper is investigated. Two different secrecy measures are considered. The first criterion is a conservative one known as joint secrecy, where the mutual leakage of all confidential messages must be small. The second criterion is a less conservative constraint known as individual secrecy, where the individual leakage of each confidential message must be small. At first, we consider the degraded multi-receiver wiretap broadcast channel and manage to establish the individual secrecy capacity region. Our encoding scheme applies a careful combination of the standard techniques of wiretap random coding and Shannon's one time pad encoding, where the confidential messages of the weak receivers are used as secret keys for the stronger ones. The validity of this technique is due to the properties of the degraded broadcast channel and the secrecy requirements of the individual secrecy criterion. Our result indicates that the individual secrecy capacity region is in fact larger than the joint one established in earlier literature. The established capacity region is then used to derive the individual secrecy capacity regions of the Gaussian single-input single-output and degraded Gaussian multiple-input multiple-output multi-receiver wiretap broadcast channels. Furthermore, we present an achievable rate region for the general two-receiver wiretap broadcast channel under both the joint and the individual secrecy criterion. Comparing these two rate regions suggests that even for the general case, the individual secrecy criterion might be able to provide a larger rate region compared with the joint one.

Improving Non-Orthogonal Multiple Access by Forming Relaying Broadcast Channels

In this letter, the performance of non-orthogonal multiple access (NOMA) with full-duplex relaying is investigated in multi-user single-input single-output downlink systems. Contrary to the original NOMA, in the proposed NOMA scheme, the base station (BS) and two served receivers within a resource block form a relaying broadcast channel (RBC), where one of the two receivers serves as a relay as well as a receiver. To analyze the performance of the proposed scheme, a simple achievable rate region of an RBC with compress-and-forward (CF) relaying is newly derived based on the noisy network coding (NNC). Furthermore, based on this, an achievable rate region of an RBC with NNC relaying when dirty-paper coding (DPC) is applied at the BS is derived. Numerical results show that the NOMA equipped with the proposed combined coding scheme comprised of DPC and NNC relaying yields significant gain over the originally proposed NOMA.

Strong converse theorems using Rényi entropies

We use a Rényi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum (or classical) communication between two parties. These include state redistribution, coherent state merging, quantum state splitting, measurement compression with quantum side information, randomness extraction against quantum side information, and data compression with quantum side information. The method we employ in proving these results extends ideas developed by Sharma [preprint arXiv:1404.5940 [quant-ph] (2014)], which he used to give a new proof of the strong converse theorem for state merging. For state redistribution, we prove the strong converse property for the boundary of the entire achievable rate region in the (e, q)-plane, where e and q denote the entanglement cost and quantum communication cost, respectively. In the case of measurement compression with quantum side information, we prove a strong converse theorem for the classical communication cost, which is a new result extending the previously known weak converse. For the remaining tasks, we provide new proofs for strong converse theorems previously established using smooth entropies. For each task, we obtain the strong converse theorem from explicit bounds on the figure of merit of the task in terms of a Rényi generalization of the optimal rate. Hence, we identify candidates for the strong converse exponents for each task discussed in this paper. To prove our results, we establish various new entropic inequalities, which might be of independent interest. These involve conditional entropies and mutual information derived from the sandwiched Rényi divergence. In particular, we obtain novel bounds relating these quantities, as well as the Rényi conditional mutual information, to the fidelity of two quantum states.

Multiuser Random Coding Techniques for Mismatched Decoding

This paper studies multiuser random coding techniques for channel coding with a given (possibly suboptimal) decoding rule. For the mismatched discrete memoryless multiple-access channel, an error exponent is obtained that is tight with respect to the ensemble average, and positive within the interior of Lapidoth's achievable rate region. This exponent proves the ensemble tightness of the exponent of Liu and Hughes in the case of maximum-likelihood decoding. An equivalent dual form of Lapidoth's achievable rate region is given, and the latter is shown to extend immediately to channels with infinite and continuous alphabets. In the setting of single-user mismatched decoding, similar analysis techniques are applied to a refined version of superposition coding, which is shown to achieve rates at least as high as standard superposition coding for any set of random-coding parameters.

On the Gaussian Fading Broadcast Relay Channel With Causal State Feedback

We investigate a typical setup of a heterogeneous network that can be modeled as a fast Rayleigh fading broadcast relay channel with one source (macrocell Base Station), one full-duplex relay (smallcell BS), and two destinations (mobile users). It is assumed that instantaneous channel state information (CSI) is available at the receivers’ side, while only a noiseless causal state feedback from the destinations about the source-to-destination channels is available at the relay. We propose a relaying scheme based on a two-stage decode-compress-forward strategy. The essential idea is to let the relay decode the source messages and then forward to the destinations a function of both the decoded messages and the CSI feedback. By characterizing and evaluating the achievable rate region of the proposed relaying scheme, we reveal that non-negligible performance gains over conventional cooperative strategies can be obtained by exploiting CSI feedback at the relay.

Spatial Modulation Exploited in Non-Reciprocal Two-Way Relay Channels: Efficient Protocols and Capacity Analysis

In this paper, the concept of spatial modulation is exploited in two-way relay channels, where two single-antenna source terminals exchange information through an assisting multi-antenna relay node, and thereby two novel transmission strategies are proposed based on the decode-and-forward protocol, aiming to achieve high throughput. One strategy is to simply engage spatial modulation in the transmissions of the relay node, whereas the other is to develop transmit diversity with spatial modulation for further benefiting from the feature of two-way relaying. Neither of the strategies requires channel state information at the transmitter and, therefore, the assumption of channel reciprocity that is commonly used in two-way relay channels can be released herein. To evaluate the performance of both proposed strategies, their capacity behaviors are analyzed and numerical comparisons are established in the metrics of achievable rate region and sum-rate. Subsequently, the first strategy, simple spatial modulation, is generalized into the two-way relaying with multi-antenna source terminals to improve the flexibility in system design and demonstrate the tractability of spatial modulation. Illustrative discussions on bit error rate not only substantiate the validity of the proposed strategies but also provide useful tools for the two-way relaying layout without the restriction of channel reciprocity.

Interference as Noise: Friend or Foe?

This paper shows that for the two-user Gaussian interference channel (G-IC) treating interference as noise without time sharing (TINnoTS) achieves the closure of the capacity region to within either a constant gap, or to within a gap of the order $O(\log ({\ln (\min ( {\mathsf {S}}, {\mathsf {I}}))}/{\gamma }))$ up to a set of Lebesgue measure $\gamma \in (0,1]$ , where $ {\mathsf {S}}$ is the largest signal to noise ratio on the direct links and $ {\mathsf {I}}$ is the largest interference to noise ratio on the cross links. As a consequence, TINnoTS is optimal from a generalized degrees of freedom (gDoF) perspective for all channel gains except for a subset of zero measure. TINnoTS with Gaussian inputs is known to be optimal within 1/2 bit for a subset of the weak interference regime. Rather surprisingly, this paper shows that TINnoTS is gDoF optimal in all parameter regimes, even in the strong and very strong interference regimes where joint decoding of Gaussian inputs is optimal. For approximate optimality of TINnoTS in all parameter regimes, it is critical to use non-Gaussian inputs. This paper thus proposes to use mixed inputs as channel inputs for the G-IC, where a mixed input is the sum of a discrete and a Gaussian random variable. Interestingly, with reference to the Han–Kobayashi achievable scheme, the discrete part of a mixed input is shown to effectively behave as a common message in the sense that, although treated as noise, its effect on the achievable rate region is as if it were jointly decoded together with the desired messages at a non-intended receiver. The practical implication is that a discrete interfering input is a friend, while an Gaussian interfering input is in general a foe. This paper also discusses other practical implications of the proposed TINnoTS scheme with mixed inputs. Since TINnoTS requires neither explicit joint decoding nor time sharing, the results of this paper are applicable to a variety of oblivious or asynchronous channels, such as the block asynchronous G-IC (which is not an information stable channel) and the G-IC with partial codebook knowledge at one or more receivers.

Simultaneously Generating Secret and Private Keys in a Cooperative Pairwise-Independent Network

This paper studies the problem of simultaneously generating a secret key (SK) and a private key (PK) between Alice and Bob, in a cooperative pairwise-independent network (PIN) with two relays. In the PIN, the pairwise source observed by every pair of terminals is independent of those sources observed by any other pairs. The SK needs to be protected from Eve, while the PK needs to be protected not only from Eve but also from the two relays. Two cooperative SK–PK generation algorithms are proposed: both of them first generate common randomness, based on the well-established pairwise key generation technique and the application of the one-time pad; but then, the two algorithms utilize the XOR operation and a specific random-binning-based SK–PK codebook to generate the expected keys, respectively. The achievable SK–PK rate regions of both the two proposed algorithms are analyzed. Of particular interest is the second algorithm with random-bing based codebook, whose achievable key rate region is demonstrated to be exactly the same as the derived outer bound, a crucial step for establishing the key capacity of this PIN model. Finally, the two proposed SK–PK generation algorithms are extended to a cooperative wireless network, where the correlated source observations are obtained from estimating wireless channels during a training phase.

Imperfect and Perfect Secrecy in Compound Multiple Access Channel With Confidential Message

In this paper, we study the problem of secret communication over a compound Multiple Access Channel (MAC). In this channel, we assume that one of the transmitted messages is confidential, which is only decoded by its corresponding receiver and kept secret from the other receiver. We call this proposed setting the compound MAC with a confidential message. For this model, we derive general inner and outer bounds for both imperfect and perfect secrecy conditions for the second receiver. Also, as examples, we investigate less noisy and Gaussian versions of this channel, and extend the results of the discrete memoryless version to these cases. Moreover, providing numerical examples for the Gaussian case, we illustrate the comparison between achievable rate regions of compound MAC and compound MAC with a confidential message. In addition, for the Gaussian case, we show that using cooperative jamming strategy can increase the achievable secrecy rate between the legitimate transmitter and the receiver.

The Approximate Capacity Region of the Symmetric <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math> </inline-formula>-User Gaussian Interference Channel With Strong Interference

The symmetric $K$ -user interference channel (IC) is studied with the goal of characterizing its capacity region in the strong interference regime within a constant gap. The achievable rate region of a scheme combining rate splitting at the transmitters and interference alignment and successive decoding/computation at the receivers is derived. Next, it is shown that this scheme achieves the so-called greedy-max corner points of the capacity region within a constant gap. By combining this result with previous results by Ordentlich et al. on the sum-capacity of the symmetric IC, a constant gap characterization of the capacity region for the strong interference regime is obtained. This leads to the first approximate characterization of the capacity region of the symmetric $K$ -user IC. Furthermore, a new scheme that achieves the sum-capacity of the channel in the strong interference regime within a constant gap is also proposed, and the corresponding gap is calculated. The advantage of the new scheme is that it leads to a characterization within a constant gap without leaving an outage set contrary to the scheme by Ordentlich et al.

On the Capacity of the Intensity-Modulation Direct-Detection Optical Broadcast Channel

The capacity of the intensity-modulation direct-detection optical broadcast channel (OBC) is investigated, under both average and peak intensity constraints. An outer bound on the capacity region is derived by adapting Bergmans’ approach to the OBC. Inner bounds are derived by using superposition coding with either truncated-Gaussian (TG) distributions or discrete distributions. While the discrete distribution achieves higher rates, the TG distribution leads to a simpler representation of the achievable rate region. At high signal-to-noise ratio (SNR), it is shown that the TG distribution is nearly optimal. It achieves the symmetric-capacity within a constant gap (independent of SNR), which approaches half a bit as the number of users grows. It also achieves the capacity region within a constant gap. At low SNR, it is shown that on–off keying (OOK) with time-division multiple-access (TDMA) is optimal. This is interesting in practice since both OOK and TDMA have low complexity. At moderate SNR (typically [0,8] dB), a discrete distribution with a small alphabet size achieves fairly good performance.

A Simple Scheme for Realizing the Promised Gains of Downlink Nonorthogonal Multiple Access

In this paper, the downlink nonorthogonal multiple access (NOMA) system is studied where purely discrete input distributions are found that achieve the capacity region to within a constant gap without successive interference cancellation (SIC). The approach is a two-step approach where the corresponding linear deterministic model is first studied and the results are then systematically translated into purely discrete input distributions for the original model. A simple yet powerful coding scheme, which adopts off-the-shelf turbo codes with pulse amplitude modulations (PAM) is then used to simulate the proposed input distributions. Simulation results show that the proposed simple scheme under turbo decoding, both with and without SIC, can operate close to information-theoretic bounds of the proposed input distributions, which lies outside the achievable rate region of any orthogonal multiple access (OMA)-type scheme.

Faster-Than-Nyquist Broadcasting in Gaussian Channels: Achievable Rate Regions and Coding

We consider the concept of faster-than-Nyquist rate (FTN) broadcasting, which nonorthogonally multiplexes more than one user message in the continuous-time domain for transmission over broadcast channels. Two FTN broadcasting approaches, namely, sub-FTN and full-FTN, are considered for broadcasting of $K$ independent messages over $K$ -user continuous time Gaussian broadcast channel. The derived achievable rate regions of the two approaches are shown to be, in general, greater than the capacity region of the optimally coded Nyquist-rate broadcasting using a same modulating pulse. The full-FTN broadcasting provides larger degrees of freedom (capacity pre-log factor) to each user of the broadcast channel while the sub-FTN improves signal-to-interference-plus-noise-ratios of the individual link. The amount of capacity gains in high SNR regime is linearly proportional to excess bandwidth in the modulating pulse used and dependent on FTN signaling rates, channel SNRs, and number of users in the broadcast channel. The simulated sub-FTN and full-FTN broadcast transceivers outperform coded Nyquist-rate systems both in BER performances and in capacity.

Impact of the relay on the coverage region of multiple‐access channels

From practical and theoretical viewpoints, performance analysis of communication systems by using information-theoretic results is important. In this study, first, the authors obtain a general achievable rate region for three-user discrete memoryless multiple-access relay channel (MARC) via partial decode and forward strategy and regular block Markov encoding/backward decoding. Also by extending the discrete alphabet results to the continuous alphabet channel, an inner bound for three-user Gaussian MARC (GMARC) is achieved. Next, based on the inner bound of three-user GMARC, they analyse the impact of a relay on the coverage region of MARC, as a basic model for uplink communications between a base station and users with the help of a relay. This analysis includes the coverage region for the multiple-access channel and two-user GMARC as special cases. Considering rate regions for the GMARC and fading GMARC, it is proved that in a fixed transmission rate, the relay extends coverage region of the MARC. Numerical illustrations confirm their theoretical results.