Capacity Region Research Articles

Biometric Identification Systems with Noisy Enrollment for Gaussian Sources and Channels.

In the present paper, we investigate the fundamental trade-off of identification, secret-key, storage, and privacy-leakage rates in biometric identification systems for remote or hidden Gaussian sources. We use a technique of converting the system to one where the data flow is in one-way direction to derive the capacity region of these rates. Also, we provide numerical calculations of three different examples for the system. The numerical results imply that it seems hard to achieve both high secret-key and small privacy-leakage rates simultaneously.

Cooperative Multiple-Access Channels With Distributed State Information

This paper studies a memoryless state-dependent multiple access channel (MAC) where two transmitters wish to convey a message to a receiver under the assumption of causal and imperfect channel state information at transmitters (CSIT) and imperfect channel state information at receiver (CSIR). In order to emphasize the limitation of transmitter cooperation between physically distributed nodes, we focus on the so-called distributed CSIT assumption, i.e., where each transmitter has its individual channel knowledge, while the message can be assumed to be partially or entirely shared a priori between transmitters by exploiting some on-board memory. Under this setup, the first part of the paper characterizes the common message capacity of the channel at hand for arbitrary CSIT and CSIR structure. The optimal scheme builds on Shannon strategies, i.e., optimal codes are constructed by letting the channel inputs be a function of current CSIT only. For a special case when CSIT is a deterministic function of CSIR, the considered scheme also achieves the capacity region of a common message and two private messages. The second part addresses an important instance of the previous general result in a context of a cooperative multi-antenna Gaussian channel under i.i.d. fading operating in frequency-division duplex mode, such that CSIT is acquired via an explicit feedback of perfect CSIR. The capacity of the channel at hand is achieved by distributed linear precoding applied to Gaussian codes. Surprisingly, we demonstrate that it is suboptimal to send a number of data streams bounded by the number of transmit antennas as typically considered in a centralized CSIT setup. Finally, numerical examples are provided to evaluate the sum capacity of the binary MAC with binary states as well as the Gaussian MAC with i.i.d. fading.

On Linearly Precoded Rate Splitting for Gaussian MIMO Broadcast Channels

In this paper, we consider a general $K$ -user Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC). We assume that the channel state is deterministic and known to all the nodes. While the private-message capacity region is well known to be achievable with dirty paper coding (DPC), we are interested in the simpler linearly precoded transmission schemes. In particular, we focus on linear precoding schemes combined with rate-splitting (RS). First, we derive an achievable rate region with minimum mean square error (MMSE) precoding at the transmitter and joint decoding of the sub-messages at the receivers. Then, we study the achievable sum rate of this scheme and obtain two findings: 1) an analytically tractable upper bound on the sum rate that is shown numerically to be a close approximation, and 2) how to reduce the number of active streams – crucial to the overall complexity – while preserving the sum rate to within a constant loss. The latter results in two practical algorithms: a stream elimination algorithm and a stream ordering algorithm. Finally, we investigate the constant-gap optimality of linearly precoded RS with respect to the capacity. Our result reveals that, while the achievable rate of linear precoding alone can be arbitrarily far from the capacity, the introduction of RS can help achieve the capacity region to within a constant gap in the two-user case. Nevertheless, we prove that the RS scheme’s constant-gap optimality does not extend to the three-user case. Specifically, we show, through a pathological example, that the gap between the sum rate and the sum capacity can be unbounded.

Understanding rabies persistence in low-density fox populations

ABSTRACT Arctic fox (Vulpes lagopus) and its tundra habitat are a unique system for the study of rabies virus epidemics. Contrary to theoretical calculations reporting a critical density (KT) of approximately 1 fox/km2 for rabies endemicity, arctic rabies persists at densities below this. The calculation of KT = 1 fox/km2 assumes uniform fox density across the landscape and unrestricted mixing between susceptible and infected foxes. We hypothesize that spatial heterogeneity arising from resource distribution or social structure may result in regions where rabies is endemic, even though average fox densities at the regional or landscape-level are below KT. To expand upon the limited body of research surrounding arctic rabies persistence, we examine arctic rabies via a two-patch structure. We find that arctic rabies can persist in heterogeneous landscapes where the mean carrying capacity is below the threshold carrying capacity required for endemicity in homogeneous landscapes. Rabies endemicity in low-carrying capacity regions within heterogeneous landscapes is further facilitated by high transmission rates, potentially due to non-breeding foxes (i.e. floaters), and when between-patch movement is restricted to latent and infected foxes. Our results suggest that rabies may persist in heterogeneous landscapes when the mean carrying capacity is as low as 0.25 foxes/km2.

A Capacity-Achieving Feedback Scheme of the Gaussian Multiple-Access Channel with Degraded Message Sets.

The classical Schalkwijk–Kailath (SK) scheme for the point-to-point white Gaussian channel with noiseless feedback plays an important role in information theory due to the fact that it is capacity-achieving and the complexity of its encoding–decoding procedure is extremely low. In recent years, it has been shown that an extended SK feedback scheme also achieves the capacity region of the two-user Gaussian multiple-access channel with noiseless feedback (GMAC-NF), where two independent messages are, respectively, encoded by two intended transmitters. However, for the two-user GMAC-NF with degraded message sets (one common message for both users and one private message for an intended user), the capacity-achieving feedback scheme remains open. In this paper, we propose a novel two-step SK-type feedback scheme for the two-user GMAC-NF with degraded message sets and show that this scheme is capacity-achieving.

Quantum broadcast channels with cooperating decoders: An information-theoretic perspective on quantum repeaters

Communication over a quantum broadcast channel with cooperation between the receivers is considered. The first form of cooperation addressed is classical conferencing, where receiver 1 can send classical messages to receiver 2. Another cooperation setting involves quantum conferencing, where receiver 1 can teleport a quantum state to receiver 2. When receiver 1 is not required to recover information and its sole purpose is to help the transmission to receiver 2, the model reduces to the quantum primitive relay channel. The quantum conferencing setting is intimately related to quantum repeaters as the sender, receiver 1, and receiver 2 can be viewed as the transmitter, the repeater, and the destination receiver, respectively. We develop lower and upper bounds on the capacity region in each setting. In particular, the cutset upper bound and the decode-forward lower bound are derived for the primitive relay channel. Furthermore, we present an entanglement-formation lower bound, where a virtual channel is simulated through the conference link. At last, we show that as opposed to the multiple access channel with entangled encoders, entanglement between decoders does not increase the classical communication rates for the broadcast dual.

Entanglement-assisted capacity regions and protocol designs for quantum multiple-access channels

We solve the entanglement-assisted (EA) classical capacity region of quantum multiple-access channels (MACs) with an arbitrary number of senders. As an example, we consider the bosonic thermal-loss MAC and solve the one-shot capacity region enabled by an entanglement source composed of sender-receiver pairwise two-mode squeezed vacuum states. The EA capacity region is strictly larger than the capacity region without entanglement-assistance. With two-mode squeezed vacuum states as the source and phase modulation as the encoding, we also design practical receiver protocols to realize the entanglement advantages. Four practical receiver designs, based on optical parametric amplifiers, are given and analyzed. In the parameter region of a large noise background, the receivers can enable a simultaneous rate advantage of 82.0% for each sender. Due to teleportation and superdense coding, our results for EA classical communication can be directly extended to EA quantum communication at half of the rates. Our work provides a unique and practical network communication scenario where entanglement can be beneficial.

Non-Orthogonal Multiple Access for Unicast and Multicast D2D: Channel Assignment, Power Allocation and Energy Efficiency.

Non-orthogonal multiple access (NOMA) techniques have emerged in the past years as a solution to approximate the throughput performance of wireless communications systems to their theoretical capacity region. We consider in this paper an optimization-based model for multicast device-to-device (MD2D) communications where the channels are not orthogonal and may be (partially or fully) shared among the transmitters in each cluster. This setting leads naturally to the introduction of NOMA transmitters and receivers who use successive interference cancellation (SIC) to separate the superposed signals. To analyze the role of NOMA in MD2D, its performance impact, potential performance gains and possible shortcomings, we formulate a model that includes SIC operations in the decoders, so that higher rates can be attained when several sources transmit on the same channel(s). We also investigate the energy efficiency of the network (global and max-min) through a dynamic power control algorithm and present a centralized and a semi-distributed solution to these optimization problems. Through numerical simulations, we show that NOMA is able to improve both the sum-rate and the max-min rate of a MD2D network even from a small degree of resource sharing. Furthermore, these gains also improve the global energy efficiency on the network, but not always the max-min energy efficiency of the devices.

Specific intracellular binding peptide as sPD-L1 antibody mimic: Robust binding capacity and intracellular region specific modulation upon applied to sensing research

Programmed death ligand 1 (PD-L1) immune checkpoint has been regarded as a new target for predicting cancer immunotherapy. As a transmembrane protein, PD-L1 has very low blood concentration and is likely to deplete their native activity when separated from the membrane environment due to significant hydrophobic domains, which make it difficult to measure sensitively. The reported PD-L1 aptamers and antibodies are both extracellular region binding molecules with the overlapping binding sites, which seriously limit with the construction of biosensor. Specific intracellular binding peptide (SIBP) as a unique PD-L1 intracellular region homing probe molecule is utilized for specifically capture targets. A simple and sensitive surface plasmon resonance (SPR) sandwich assay was constructed to detect serum soluble PD-L1 (sPD-L1) based on the unique and strong binding ability of SIBP to the intracellular region of sPD-L1. The designed SPR sensor showed great selectivity and wide dynamic response range of sPD-L1 concentration from 10 ng/mL to 2000 ng/mL. The limit of detection was calculated to be 1.749 ng/mL (S/N = 3). Owing to the SIBP's strong and specific binding ability with sPD-L1, the sensitive sensor can successfully detect sPD-L1 in serum samples, paving the way for the development of efficient test tools for clinical diagnosis and analysis.

Physical Layer Computation as NOMA for Integrated Wireless Systems

We consider two users A and B wanting to exchange their messages M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</sub> and M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> via a relay in a wireless communication network. To this aim, we have two methods: direct forward (DF) and computation and forward (CAF). In the first method, after an orthogonal multiple access (OMA) or non-orthogonal multiple access (NOMA) phase, the receiver decodes the two messages. In the second method, after a NOMA phase, the receiver decodes only the (modulo) sum. In the latter case the capacity region (computation region) is not known. This paper compares the two methods. To such aim, we propose a unified coding framework and identify a lower bound of achievable computation rates. We consider three constellations for the symmetric two-user Gaussian channel with Eisenstein constellation showing highest performance. We also show that a minimum signal-to-noise ratio is required for our CAF method to outperform DF, and we obtain the numerical values of such minimum ratios for the three constellations. Finally, we show achievability of our bounds, which is proved to require affine codes for computation, which has not been proved before. Overall, our results are useful for communication system designers towards practical implementation of multiple access methods in integrated wireless systems.

On the Capacity Region of Bipartite and Tripartite Entanglement Switching

We study a quantum switch serving a set of users in a star topology. The function of the switch is to create bipartite or tripartite entangled state among users at the highest possible rates at a fixed ratio. We model a set of randomized switching policies. Discovering that some are better than others, we present analytical results for the case where the switch stores one qubit per user, and find that the best policies outperform a time division multiplexing (TDM) policy for sharing the switch between bipartite and tripartite state generation. This performance improvement decreases as the number of users grows. The model is easily augmented to study the capacity region in the presence of qubit decoherence, obtaining similar results. Moreover, decoherence appears to have little effect on capacity. We also study a smaller class of policies when the switch stores two qubits per user.

On the Capacity Regions of Cloud Radio Access Networks With Limited Orthogonal Fronthaul

Uplink and downlink cloud radio access networks are modeled as two-hop ${K}$ -user ${L}$ -relay networks, whereby small base-stations act as relays for end-to-end communications and are connected to a central processor via orthogonal fronthaul links of finite capacities. Simplified versions of network compress–forward (or noisy network coding) and distributed decode–forward are presented to establish inner bounds on the capacity region for uplink and downlink communications, that match the respective cutset bounds to within a finite gap independent of the channel gains and signal to noise ratios. These approximate capacity regions are then compared with the capacity regions for networks with no capacity limit on the fronthaul. Although it takes infinite fronthaul link capacities to achieve these “fronthaul-unlimited” capacity regions exactly, these capacity regions can be approached approximately with finite-capacity fronthaul. The total fronthaul link capacities required to approach the fronthaul-unlimited sum-rates (for uplink and downlink) are characterized. Based on these results, the capacity scaling law in the large network size limit is established under certain uplink and downlink network models, both theoretically and via simulations.

Strong Coordination Over Noisy Channels

We study the problem of strong coordination of the actions of two nodes $X$ and $Y$ that communicate over a discrete memoryless channel (DMC) such that the actions follow a prescribed joint probability distribution. We propose two novel random coding schemes and a polar coding scheme for this noisy strong coordination problem, and derive inner bounds for the respective strong coordination capacity region. The first scheme is a joint coordination-channel coding scheme that utilizes the randomness provided by the DMC to reduce the amount of local randomness required to generate the sequence of actions at Node $Y$. Based on this random coding scheme, we provide a characterization of the capacity region for two special cases of the noisy strong coordination setup, namely, when the actions at Node $Y$ are determined by Node $X$ and when the DMC is a deterministic channel. The second scheme exploits separate coordination and channel coding where local randomness is extracted from the channel after decoding. The third scheme is a joint coordination-channel polar coding scheme for strong coordination. We show that polar codes are able to achieve the established inner bound to the noisy strong coordination capacity region and thus provide a constructive alternative to a random coding proof. Our polar coding scheme also offers a constructive solution to a channel simulation problem where a DMC and shared randomness are employed together to simulate another DMC. Finally, by leveraging the random coding results for this problem, we present an example in which the proposed joint scheme is able to strictly outperform the separate scheme in terms of achievable communication rate for the same amount of injected randomness into both systems. Thus, we establish the sub-optimality of the separation of strong coordination and channel coding with respect to the communication rate over the DMC.

Dynamic Bandwidth Part Allocation in 5G Ultra Reliable Low Latency Communication for Unmanned Aerial Vehicles with High Data Rate Traffic.

The 3GPP standardized the physical layer specification in 5G New Radio to support enhanced mobile broadband (eMBB) and ultra-reliable low-latency communication (URLLC) coexistence in usage scenarios including aerial vehicles (AVs). Dynamic multiplexing of URLLC traffic was standardized to increase the outage capacity. DM allocates a fully overlapped bandwidth part (BWP) of eMBB and URLLC AVs to perform the immediate scheduling of URLLC traffic by puncturing ongoing eMBB traffic. However, DM often suffers from a significant frame error incurred by puncturing. Meanwhile, BWP can be sliced orthogonally for eMBB and URLLC AVs, possibly preventing overdimensioning the resources depending on the eMBB and URLLC traffic loads. In this paper, we propose a dynamic BWP allocation scheme that switches between two multiplexing methods, dynamic multiplexing (DM) and orthogonal slicing (OS), so as to minimize an impact of uRLLC traffic on eMBB traffic. To implement efficient BWP allocation, the capacity region is analyzed by considering the effect of physical layer parameters, such as modulation and coding scheme (MCS) levels and code block group size on DM and OS. OS is effective for improving the eMBB throughput under a URLLC latency constraint for deterministic and predictable URLLC traffic, whereas DM has limited error-correcting capability against the URLLC’s puncturing effect. The relative MCS level of eMBB and URLLC is critical in determining the eMBB traffic tolerance against puncturing. Identifying the performance tradeoff between DM and OS, the tolerance level is quantified by a URLLC load threshold. It is given in an approximate closed form, which is an essential reference for selecting DM over OS, enabling dynamic BWP allocation for the URLLC AV.

Capacity Analysis of Non-Orthogonal Multiple Access for Uplink and Downlink

Non-orthogonal multiple access (NOMA) is intended to be used for the next generation 5G cellular networks. In this paper, the expressions for the channel capacities for symmetric and asymmetric NOMA networks have been analysed. The performance measure of user spectral efficiency and the sum-rate bounds, for the NOMA and the existing orthogonal multiple access (OMA) networks have been compared. Furthermore, analysis of user rate and capacity of NOMA network has been carried out and it is observed that the NOMA capacity region varies as a function of the power allocation factor. The corresponding models have been developed for both uplink and downlink, and simulated with MATLAB. The NOMA performance with imperfect Successive Interference Cancellation (SIC) decoding is also analysed for the downlink. It is also verified that the transmit power may be increased to counter the spectral efficiency reduction due to imperfect SIC.

Power Efficient IRS-Assisted NOMA

In this paper, we propose a downlink multiple-input single-output (MISO) transmission scheme, which is assisted by an intelligent reflecting surface (IRS) consisting of a large number of passive reflecting elements. In the literature, it has been proved that nonorthogonal multiple access (NOMA) can achieve the same performance as computationally complex dirty paper coding, where the quasi-degradation condition is satisfied, conditioned on the users' channels fall in the quasi-degradation region. However, in a conventional communication scenario, it is difficult to guarantee the quasi-degradation, because the channels are determined by the propagation environments and cannot be reconfigured. To overcome this difficulty, we focus on an IRS-assisted MISO NOMA system, where the wireless channels can be effectively tuned. We optimize the beamforming vectors and the IRS phase shift matrix for minimizing transmission power. Furthermore, we propose an improved quasi-degradation condition by using IRS, which can ensure that NOMA achieves the capacity region with high possibility. For a comparison, we study zero-forcing beamforming (ZFBF) as well, where the beamforming vectors and the IRS phase shift matrix are also jointly optimized. Comparing NOMA with ZFBF, it is shown that, with the same IRS phase shift matrix and the improved quasi-degradation condition, NOMA always outperforms ZFBF. At the same time, we identify the condition under which ZFBF outperforms NOMA, which motivates the proposed hybrid NOMA transmission. Simulation results show that the proposed IRS-assisted MISO system outperforms the MISO case without IRS, and the hybrid NOMA transmission scheme always achieves better performance than orthogonal multiple access.

Fundamental Limits of Biometric Identification System Under Noisy Enrollment

The fundamental limits of biometric identification systems under a strong secrecy criterion are investigated. In the previous studies of this scenario, the fundamental trade-off among secrecy, template, privacy- and secrecy-leakages has been revealed in the case where there is only one user, while the case of multiple users has not been discussed yet. In this study, we consider the system with exponentially many users, and we characterize the capacity region of the rate tuples including the user (identification) rate under the strong secrecy criterion. In the achievability proof, we derive a new method to incorporate multiple users by extending the random binning for one user's case. The obtained result shows that the characterization of the capacity region does not vary regardless of the weak or strong secrecy criterion in terms of secrecy-leakage.

Inner Bounds for the Almost Entropic Region and Network Code Construction

In the fields of information theory and network coding, a complete characterization of the almost entropic region is a fundamental but inherently difficult open problem. This paper focuses on the characterization of this region via explicit inner bounds, optimization of functions over this region, and network code construction. One approach to study the entropic region is to put a constraint on the alphabets for involved random variables, enabling us to focus on a specific set of joint distributions. We present the notion of alphabet constrained entropic set and describe its properties, namely, its a closed and path-connected set. Motivated by the properties, a random local search algorithm is designed to find an entropic vector and associated distribution near to a given target vector and extended to optimize functions of joint entropies. We present significantly improved inner bound compared to known inner bounds for the almost entropic region involving four random variables using a refinement of our algorithm. Finally, another application of the algorithm is shown to construct network codes and index codes for a given rate vector in the capacity region. This approach to constructing network codes is novel and has an entirely different flavor than classical coding theoretic construction.

A general achievable rate region and two certain capacity regions for Slepian–Wolf multiple‐access relay channel with non‐causal side information at one encoder

A general achievable rate region and two certain capacity regions for Slepian–Wolf multiple‐access relay channel with non‐causal side information at one encoder

Capacity Limits of Full-Duplex Cellular Network

This paper aims to characterize the capacity limits of a wireless cellular network with a full-duplex (FD) base-station (BS) and half-duplex user terminals, in which three independent messages are communicated: the uplink message $m_1$ from the uplink user to the BS, the downlink message $m_2$ from the BS to the downlink user, and the device-to-device (D2D) message $m_3$ from the uplink user to the downlink user. From an information theoretical perspective, the overall network can be viewed as a generalization of the FD relay broadcast channel with a side message transmitted from the relay to the destination. We begin with a simpler case that involves the uplink and downlink transmissions of $(m_1,m_2)$ only, and propose an achievable rate region based on a novel strategy that uses the BS as a FD relay to facilitate the interference cancellation at the downlink user. We also prove a new converse, which is strictly tighter than the cut-set bound, and characterize the capacity region of the scalar Gaussian FD network without a D2D message to within a constant gap. This paper further studies a general setup wherein $(m_1,m_2,m_3)$ are communicated simultaneously. To account for the D2D message, we incorporate Marton's broadcast coding into the previous scheme to obtain a larger achievable rate region than the existing ones in the literature. We also improve the cut-set bound by means of genie and show that by using one of the two simple rate-splitting schemes, the capacity region of the scalar Gaussian FD network with a D2D message can already be reached to within a constant gap. Finally, a generalization to the vector Gaussian channel case is discussed. Simulation results demonstrate the advantage of using the BS as relay in enhancing the throughput of the FD cellular network.