While there exists a great body of research on reflection optimization of a reconfigurable intelligent surface (RIS), these optimizations assume independent phase shift and amplitude for the RIS reflection coefficients. Moreover, the choice of phase is typically assumed to be continuous over the full range. In practice, the phase shift and the amplitude are coupled, and the phase choices are limited to a discrete set. In our work, we consider a practical RIS model with coupled phase shift and amplitude and limited phase choices. For the coupled RIS model, given a configuration set (which is a discrete set of coupled reflection coefficient choices that an RIS element can take), we develop an efficient method for capacity maximization by finding the optimal reflection coefficients of the RIS elements. Our method has a complexity linear with the number of RIS elements and the number of discrete reflection coefficient choices. We also develop a method that optimally selects the configuration set of the system.

In large-scale distributed matrix-vector multiplications, e.g., for generative AI, straggling nodes can slow down or even jeopardize the whole operation. Coded distributed computing (CDC) uses erasure codes to create redundant computations and combat stragglers. This requires encoding very large matrices. Moreover, encoding must be repeated whenever system parameters (e.g., weight matrices in AI models) evolve. This paper introduces a general framework for reducing encoding complexity in CDC. We propose the notion of an encoding blueprint, a construction schedule that specifies how each coded symbol is constructed from data and previously computed coded symbols. An optimal blueprint minimizes the number of arithmetic operations required for a given code. We first design blueprints using addition-only operations. We then extend the framework to also allow subtraction, which further decreases the number of required operations. The optimization problem is cast as a mixed-integer program (MIP), and solved. Numerical results on matrix–vector multiplication show that optimized blueprints reduce encoding operations by up to 60 percent compared to standard methods, saving billions of operations in large-scale applications. Our techniques can be used for efficient decoding as well.

In high-rate or long-haul optical fiber transmissions, correcting chromatic dispersion (CD) is critical but challenging and energy-intensive due to the large filter tap size required for CD compensation (CDC). Overlap-save (OLS) is a common frequency-domain CDC technique that uses fast Fourier transform (FFT). However, hardware constraints-such as power, memory, latency, and chip area-limit the FFT size. This limitation makes OLS too complex or even infeasible in dispersive channels where the number of taps approaches or exceeds the FFT size. We introduce the time-segmented overlap-free (TS-OLF) technique, a novel frequency-domain block filtering method to enable low-complexity CDC under FFT-size limitations. TS-OLF divides the signal into non-overlapping blocks and segments the filter accordingly to enable filtering operations with any FFT size. It aggregates the results of different filter segments directly in the frequency domain, therefore, using a minimum number of FFT operations. We show that TS-OLF achieves consistently lower complexity than OLS when the filter size is more than half the FFT size, and unlike OLS, can handle filter sizes that exceed the FFT size. TS-OLF also outperforms other filter segmenting methods, providing significant complexity improvements.

According to the Gaussian noise (GN) model, nonlinear interference noise (NLIN) in fiber depends on the signal power spectral density (PSD). Consequently, optimizing the PSD of the pulse that modulates data, as the main factor influencing the PSD of the launched signal into the fiber, can effectively minimize fiber NLIN. In this study, we first employ the calculus of variations to identify the optimal band-limited pulse PSD that minimizes fiber NLIN. Next, we add other communication requirements, such as zero inter-symbol interference (ISI) and fast decay over time, as constraints to our design problem. For this case, we develop a general pulse model and formulate the design problem as an optimization problem. By solving this optimization problem, we find the optimal pulse PSD that not only minimizes NLIN power in fiber but also meets practical requirements. We study the time-domain impact of the designed modulating pulse PSD on the launched signal properties to gain insights into the nonlinearity benefits we achieve. We further analytically demonstrate that our designed pulse has favorable properties for the Godard timing recovery method. Through extensive simulations using the split-step Fourier method on a fiber with typical parameters and considering practical transmitter/receiver limitations, we illustrate the superior system reach and achievable data rate of our optimized pulses compared to existing pulse shapes.

Non-binary polar codes (NBPCs) decoded by successive cancellation (SC) algorithm have remarkable bit-error-rate performance compared to the binary polar codes (BPCs). Due to its serial nature, SC decoding suffers from long latency. The latency issue in BPCs has been the topic of extensive research and it has been notably resolved by the introduction of fast SC-based decoders. However, the latency problem of NBPCs is mainly untouched and the vast majority of research on NBPCs is devoted to issues concerning design and efficient implementation. In this paper, we propose fast SC decoding for NBPCs constructed based on$2\times 2$kernels. In particular, we extend the special nodes of BPCs to their non-binary counterpart and define various non-binary special nodes in the SC decoding tree of NBPCs and propose their fast decoding. This way, we avoid traversing the full decoding tree and significantly reduce the decoding delay compared to symbol-by-symbol SC decoding. We also propose a simplified NBPC structure that facilitates the procedure of non-binary fast SC decoding. Using our proposed fast non-binary decoder, we observe an improvement of more than 96% in latency concerning the original SC decoding. This is while our proposed fast SC decoder for NBPCs incurs no error-rate loss.

This paper introduces an innovative multi-queue fog architecture coupled with an intelligent controller, aimed at enhancing the efficiency and adaptability of fog computing environments. Unlike conventional single-queue fog architectures that typically rely on basic first-in-first-out (FIFO) task execution models in fog servers, our approach offers heightened granularity and flexibility in task scheduling. This feature enables effective task management, catering specifically to Internet of Things (IoT) applications characterized by varying degrees of time-sensitivity and resource requirements. Our proposed deep weighted-fair fog servers (DeepWFFS) scheme comprises two key elements: the weighted-fair fog server (WFFS) framework and an intelligent deep controller (DC) leveraging deep reinforcement learning (DRL) for task prioritization. The WFFS framework adopts multiple queues within fog servers, each assigned a predefined weight representing task priority. This prevents task starvation and promotes equitable task execution. Meanwhile, the DC continuously monitors task workloads and priorities, ensuring optimal task allocation to the most suitable queues within fog and cloud servers. Through simulation, our results exhibit the superior performance of DeepWFFS compared to benchmark schemes. This advancement showcases the potential of our architecture to efficiently manage diverse tasks in fog computing environments.

In distributed computing systems, to mitigate the adverse effect of stragglers on the computation time, computation redundancy is used. The redundancy can be added proactively at the beginning, or reactively after some time based on the delay pattern of the workers. While most of the existing work with reactive mitigation strategy only considered task replication, we propose a coded reactive straggler mitigation with an uncoded and a coded phase for distributed matrix-matrix multiplications. Specifically, in the uncoded phase of the proposed strategy, the master distributes the computational job without redundancy among the workers. After a predetermined waiting time, the master cancels the remaining tasks. It then encodes the remaining tasks and distributes them among the workers. In the uncoded phase, in addition to the conventional erasure model, where workers can communicate only once, we consider multi-message communication (MMC) model to exploit the partial works done by workers. The optimum waiting time for the uncoded phase and the optimum code rate for the coded phase are also obtained. Our simulation results demonstrate that the proposed coded reactive mitigation significantly decreases the execution time in comparison with both the proactive mitigation strategy or the existing reactive mitigation strategy.

We address the reflection optimization problem for a reconfigurable intelligent surface (RIS), where the RIS elements feature a set of non-uniformly spaced discrete phase shifts. This is motivated by the actual behavior of practical RIS elements, where it is shown that a uniform phase shift assumption is not realistic. A problem is formulated to find the optimal reflection amplitudes and reflection phase shifts of the RIS elements such that the channel capacity of the target user is maximized. We first prove that in the optimal configuration, each RIS element is either turned off or operates at maximum amplitude. We then develop a method that finds the optimal reflection amplitudes and phases with complexity linear with the number of RIS elements. An interesting insight into the reflection optimization problem is also provided.

One of the main bottlenecks in distributed computing systems is the stragglers’ problem. Error correction codes have been proposed to alleviate this problem at the cost of coding complexity for the master node. In this work, we aim to reduce this coding complexity and propose a novel family of binary locally repairable codes (BLRC) to encode the distributed tasks in a linear matrix-vector multiplication problem. In comparison to the widely used maximum distance separable (MDS) codes, our proposed codes (i) eliminate the costly multiplication operations from the encoding and decoding processes, (ii) allow for low-complexity recovery within the local groups. We analyze the complexity of our proposed codes and through simulations show that compared to MDS codes, our codes reduce the overall encoding plus computation plus decoding time by more than 35% in many practical scenarios.

The zero padding (ZP) variants of orthogonal frequency-division multiplexing (OFDM) exhibit a lower bit error rate (BER) and higher energy efficiency compared to their cyclic prefix (CP) counterparts. However, the employment of ZP-OFDM demands strict time synchronization, which is challenging in the absence of pilots or CP. Moreover, time synchronization in OFDM systems is even more challenging when impulsive noise is present. It is well known that urban noise, which consists largely of impulsive noise generated by spark plugs used in internal combustion engines, switching and industrial activities, and discharge of high voltage distribution lines, has a strong influence on digital mobile communications. In this paper, we propose a new low-complexity approximate maximum likelihood (A-ML) timing offset (TO) estimator for ZP multiple-input multiple-output (MIMO)-OFDM in impulsive-noise environments. Performance comparison of the A-ML estimator with existing TO estimators demonstrates a superior performance in terms of lock-in probability with similar computational complexity. Also, compared to the optimal ML TO estimator, it offers a significantly lower computational complexity with negligible performance loss. The A-ML estimator can be employed for both frame and symbol synchronization.

Digital backpropagation (DBP) is the most effective fiber optic compensation technique. While DBP can increase the achievable data rate, its high computational complexity prevents its use in real-time applications. Parallelization is one of the most promising techniques to allow real-time DBP. Existing parallel DBP (PDBP) are based on coupled nonlinear Schrodinger equation (NLSE), which only considers cross-phase modulation and discards the rest of the inter-channel impairments. Therefore, these methods lose their performance in today's wavelength-division multiplexing systems. We fill this gap by proposing a PDBP capable of working with regular NLSE and compensating for all fiber impairments, including four-wave mixing. We analytically derive the compensation equations for the parallel scheme and handle them efficiently to reduce the complexity. Our simulations show a significant improvement in the sense of optimal launched power, achievable data rate, and system reach over existing DBPs with comparable complexity.

In distributed computing systems, to mitigate the adverse effect of stragglers on the computation time, computation redundancy is used. The redundancy can be added proactively at the beginning, or reactively after some time based on the delay pattern of the workers. While most of the existing work with reactive mitigation strategy only considered task replication, we propose a coded reactive straggler mitigation with an uncoded and a coded phase for distributed matrix-matrix multiplication. Specifically, in the uncoded phase of the proposed reactive strategy, the master distributes the computational job without redundancy among workers and waits for some time. After the waiting time, the master cancels the remaining tasks. It then encodes the remaining tasks and distributes them among the workers that have already completed their computations. The expected execution time of the proposed method is analytically obtained. Furthermore, the optimal waiting time for the uncoded phase and the optimal code rate for the coded phase are investigated. Our simulation results demonstrate that the proposed coded reactive mitigation strategy significantly decreases the execution time in comparison with the proactive mitigation strategy or repetition-based reactive mitigation strategy.

We propose a hybrid probabilistic-geometric constellation shaping method for optical fiber communication systems that is non-linearity tolerant and compatible with probabilistic fold shaping (PFS) architecture. To do so, the impact of non-linear interference noise (NLIN) in the shaping process is considered. This is a challenging process because NLIN is itself constellation dependent. This study copes with this issue by developing a deep learning-based shaping method that takes the enhanced Gaussian noise (EGN) model of fiber into account to model NLIN. Our hybrid shaping scheme maximizes the generalized mutual information (GMI) rate of the optical system while the impacts of shaping on the NLIN power are considered. Our results show that the proposed hybrid scheme results in significant reach improvements and outperforms recent hybrid shaping methods. Interestingly, our hybrid shaping scheme suggests distributions that are much different from the traditional Maxwell-Boltzmann distributions.

In this paper, we introduce the DRJLRA algorithm, a load and resource allocation scheme based on deep reinforcement learning (DRL) for a generic multi-master, multi-worker coded distributed computing (CDC) system. Our aim is to minimize the combined delay of communication and computation for a set of matrix-vector multiplication tasks. The proposed DRL-based approach has several unique features that set it apart from existing literature. Firstly, it is applicable to general CDC systems with multiple masters and workers. Additionally, it considers multi-task CDC systems with stochastic task arrivals, takes into account the heterogeneity of workers with random computation and communication delays, and utilizes the state-of-the-art soft actor-critic (SAC) DRL algorithm, making it versatile and efficient in handling complex and dynamic CDC environments. Our results demonstrate that DRJLRA outperforms benchmark schemes significantly. It is thus well-suited for real-world CDC systems with diverse and dynamic workloads.

This article studies the network lifetime optimization problem in a multiuser mobile-edge computing (MEC)-enabled Internet of Things (IoT) system comprising an access point (AP), a MEC server, and a set of$K$mobile devices (MDs) with limited battery capacity. Considering the residual battery energy at the MDs, stochastic task arrivals, and time-varying wireless fading channels, a soft actor–critic (SAC)-based deep reinforcement learning (DRL) lifetime maximization, called DeepLM, is proposed to jointly optimize the task splitting ratio, the local CPU-cycle frequencies at the MDs, the bandwidth allocation, and the CPU-cycle frequency allocation at the MEC server subject to the task queuing backlogs constraint, the bandwidth constraint, and maximum CPU-cycle frequency constraints at the MDs and the MEC server. Our results reveal that DeepLM enjoys a fast convergence rate and a small oscillation amplitude. We also compare the performance of DeepLM with three benchmark offloading schemes, namely, fully edge computing (FEC), fully local computing (FLC), and random computation offloading (RCO). DeepLM increases the network lifetime by 496% and 229% compared to the FLC and RCO schemes. Interestingly, it achieves such a colossal lifetime improvement when its nonbacklog probability is 0.99, while that of FEC, FLC, and RCO is 0.69, 0.53, and 0.25, respectively, showing a significant performance gain of 30%, 46%, and 74%.

Distributed computing systems have been widely used in recent years to handle massive computations required by newly emerged machine learning algorithms and signal processing problems. In practice, a distributed computing system often receives multiple tasks each needs to be finished by a specific deadline. This necessitates use of a task scheduler which orders and prioritizes tasks executions. In this work, we consider task scheduling for a homogeneous distributed computing system with multiple matrix-vector multiplication jobs, and try to maximize the number of tasks completed before their deadlines. The main challenges in such a system are random task arrivals and random execution times due to the straggling effect. To address these challenges, we propose two task scheduling algorithms namely “simple greedy” and “farsighted greedy” and compare their performance with the ultimate upper bound, i.e., a genie-aided algorithm that knows the exact arrival and execution times of all tasks. Our simulation results demonstrate that the proposed algorithms can approach the performance of the genie-aided algorithm.

In distributed computing, when a large number of helper nodes assist a master node to finish a large task, the main challenge is when some of these helpers straggle. Several coded distributed computing schemes exist that resolve the straggling problem. In these solutions, however, the decoding remains a responsibility of the master node. The complexity of decoding can be significant and increase the execution time considerably. In this work, we propose a multilayer coding strategy that allows some helpers to assist with the decoding. With this multilayer structure, the original decoding is performed by some decoding helpers, and the master only minimally participates in decoding to make every layer reliable. The optimization problem to minimize the overall completion time is also studied and shown to have a simple solution in almost all practical scenarios.

We study the performance of a network-coded cooperative (NCC) system in an underlay cognitive radio network (CRN). The primary network (PN) consists of a single transmitter-receiver pair, and the secondary network (SN) is an NCC system with$N$users,$M$relays, and a single destination. The relays employ decode-and-forward (DF) protocol and use network coding (NC). We study the performance of the SN under two types of power constraints: i) the combined peak interference power constraint on the PN and maximum transmit power constraint at the SN; and ii) the single peak interference power constraint on the PN. For the SN, an exact closed-form expression and an asymptotically tight end-to-end outage probability are derived, and the diversity order and coding gain are quantified. Compared to the existing literature, the proposed CRN NCC has four main distinguishable features: i) it applies to general CRN NCC network settings with an arbitrary number of users and relays; ii) it considers general relay selection mechanism and independent and non-identically distributed (i.n.i.d.)$Nakagami-m$fading channels; iii) it assumes secondary-to-primary and primary-to-secondary interference links; and iv) it provides a generalization of previous work and includes existing results in the literature as special cases.

This paper investigates the performance of a network-coded cooperative (NCC) system in an underlay cognitive radio network (CRN). The primary network (PN) consists of a single transmitter-receiver pair, while the secondary network (SN) is composed of N sources, a single destination, and M decode-and-forward (DF) relays, employing network coding (NC) over non-binary Galois field. For the SN, a closed-form expression and an asymptotically tight end-to-end (E2E) outage probability (OP) are derived and the diversity order is quantified. Compared to the existing literature, the proposed CRN NCC has four main distinguishable features: i) it is applicable to general CRN NCC network settings with arbitrary number of sources and relays; ii) it considers general relay selection and independent and non-identically distributed (i.n.i.d.) Nakagami-m fading channels; iii) it accounts for maximum transmit power at the SN and assumes secondary-to-primary (S2P) and primary-to-secondary (P2S) interference links; and iv) it provides a generalization of previous works and includes existing results in the literature as special cases. Simulation results are further provided to confirm the correctness of our analysis.

Non-line-of-sight (NLOS) error is one of the dominant sources of error in localization applications. Existing algorithms rely on solving a set of highly nonlinear equations to compensate for this error, which is intractable in practice. In this paper, we propose an efficient NLOS identification algorithm based on supervised machine learning. This approach enables us to improve localization accuracy by taking advantage of the NLOS measurements if the location of the reflector is known. Hence, our approach can be employed in combination with 5G intelligent reflecting surface systems to provide location-based wireless services. We also analytically derive the Cramer-Rao lower bound for the localization problem at hand. Finally, we investigate the performance of our proposed NLOS identification algorithm under different simulation setups.

In this paper, a statistical-based sphere decoding with increasing radius search (S-SD-IRS) algorithm is proposed, where the radiuses of the decoding hyperspheres are determined based on the statistical properties of the communication channel and additive noise. We show that the probability density functions (PDFs) of the q lowest squared distances in the closest lattice point problem can be approximated by Gumbel distributions with different parameters. Based on the obtained PDFs and by considering the characteristics of the fading channels and additive noise, we choose the radiuses for sphere decoding more efficiently than the conventional methods that ignore the characteristics of system. The performance achieved by the proposed algorithm is very close to the optimal maximum likelihood decoding (MLD) over a wide range of signal-to-noise ratios (SNRs), while the computational complexity, compared to existing sphere decoding variants, is significantly reduced. It is shown that the average number of lattice points inside the decoding hyperspheres drastically reduces in the proposed S-SD-IRS algorithm.

Sparse signals are encountered in many modern technologies. Compressed sensing methods create the opportunity of sampling sparse signals significantly lower than the Nyquist rate. However, sparse signal recovery still remains a challenge. In this work, we show that detecting the support of the sparse signal can be viewed as a classification problem, and hence efficiently be solved using neural networks (NN). We find the best NN configuration in support detection for random data sets, where an accuracy of 98% is achieved in highly sparse signals. After detecting the support of the signal, we show that signal recovery can be done efficiently. In this work, we develop two recovery methods. The simulation studies confirm that our proposed methods outperform counterpart algorithms in both accuracy and convergence speed.

Non-binary kernels are used to improve the length flexibility of polar codes. Given the long decoding latency of the successive-cancellation (SC) decoder, devising fast decoding solutions for non-binary kernels is necessary. In this work, we identify a new node in the decoding tree of polar codes which are constructed by commonly used ternary kernels. We call this t-dimensional SPC (tD-SPC) node and propose a low-complexity decoder for it. Moreover, we adapt a node introduced for binary kernel to be used in the fast SC decoding of the 3×3 kernel polar codes. Simulation results show that implementing the proposed fast decoders can reduce the decoding latency by more than 40% if a performance loss of just 0.5 dB is tolerated.

We study the effect of outdated channel state information (CSI) and co-channel interference (CCI) on the performance of relay selection (RS) network-coded cooperative (NCC) multiple-input multiple-output (MIMO) systems. Specifically, we consider a RS MIMO-NCC system where N single-antenna sources communicate with one multiple-antenna destination using M decode-and-forward (DF) multiple-antenna relays. The destination selects K best relays according to the quality of relay-destination channels. The selected relays apply network coding (NC) on the received sources' symbols using network code coefficients based on maximum distance separable (MDS) codes. The exact closed-form outage probability (OP) of the system is derived. The asymptotic high signal-to-noise ratio (SNR) OP is also obtained, through which the diversity order and the coding gain are found. Numerical results are further presented to illustrate the adverse effect of outdated CSI and CCI on the system performance and to validate the accuracy of our analysis.

Deep neural networks (DNN) have gained considerable attention in the communication literature during the past few years. In particular, as a well-known DNN architecture, autoencoders (AE) are used to model the end-to-end communication systems achieving a reasonable performance in terms of block error rate (BLER). However, autoencoders significantly suffer from high peak-to-average-power-ratio (PAPR), resulting in power amplifier saturation. This paper proposes a novel DNN architecture for reducing PAPR in autoencoder-based communication systems. Simulation results verify that the proposed scheme outperforms the conventional PAPR reduction method, i.e., loss function-based PAPR reduction approach, in terms of both bit error rate (BER) and PAPR.

For a multi-way relay network (MWRN) with K users, K time slots are needed for full data exchange. Thus, the overall spectral efficiency, due to the 1/K pre-log factor, declines as number of users grows. It has recently been improved to roughly K/2 time slots, but even this improvement does not arrest the decline. Herein, we reduce this task to just two time slots regardless of K. To do this, we exploit the performance gains of non-orthogonal multiple-access (NOMA) and a massive multiple-input multiple-output (MIMO) relay. First, the users transmit their signals to the relay, which uses maximal ratio combining reception. Next, the relay transmits a superposition-coded signal for all users by using maximal ratio transmission. Each user then performs successive interference cancellation (SIC) decoding of data symbols of the other K - 1 user nodes. We use the so-called worst-case Gaussian approximation to derive the overall sum rate and demonstrate significant spectral-efficiency gains and energy-efficiency gains over the existing MWRN counterparts. We also design the relay power allocation matrix to maximize the minimum among the user rates, thus maximizing the user fairness. Furthermore, the effects of imperfect SIC and imperfect channel state information (CSI) on the sum rate are analyzed.

In distributed computing, a number of available helper nodes assist in completing a task for the master node. In such setups, the failure or straggling of even a single helper node can significantly increase the processing time. Therefore, coded distributed computing has been the subject of many recent studies. A problem that arises in some setups is that the master's decoding complexity may exceed the complexity of self-computation, rending distributed computing useless. One such case is distributed large-scale FFT, where many helper nodes are required. In this work, we propose a novel distributed coded FFT, where the master's load is significantly lower than the existing work. The gain is obtained by (1) using a novel distributed FFT structure which allows for reliable distributed coding at the Shuffle stage, and (2) using Raptor codes which enjoy a linear complexity at the cost of a small number of extra helper nodes. Numerical results are provided to support the benefits of our proposed solution and to optimize design parameters.

We consider a network-coded cooperative (NCC) system that consists of N ≥ 2 sources, M ≥ 1 decode- and-forward (DF) relays, and a single destination. The relays perform network coding (NC) on the received sources' symbols using maximum distance separable (MDS) codes. For this system, we propose the most generalized user-relay selection (GURS) scheme in the literature that selects any arbitrary subsets of K users and any arbitrary subsets of L relays subject to practical constraints such as load balancing conditions and scheduling policy. Our analytical results and design guidelines generalize and subsume all existing results as special cases. To this end, we derive a new closed-form outage probability (OP) expression, assuming non-identically and independently distributed (n.i.i.d.) Rayleigh fading channels. The asymptotic outage expression at high signal-to-noise ratio (SNR) regime is further derived, based on which, the achievable diversity order and coding gain are quantified. The theoretical derivations are also validated through Monte-Carlo simulation.

High power consumption and hardware cost have motivated using low-resolution analog-to-digital converters (ADCs) for practical massive multiple-input multiple-output (mMIMO) systems. In this paper, we consider a general mMIMO multi-way relaying system with a multi-level mixed-ADC architecture in which each antenna is connected to an ADC pair with an arbitrary resolution. By leveraging on Bussgang's decomposition theorem and Lloyd-Max algorithm for quantization, tight closed-form approximations are derived for the average achievable rates of zero-forcing (ZF) relaying considering both perfect and imperfect channel state information (CSI). To handle such a challenging setup, we develop a novel method for the achievable rate analysis using distributions of the singular values of Gaussian matrices and properties of Haar matrices. We demonstrate that the average achievable rate has an almost linear relation with the square of the average of quantization coefficients pertaining to the ADC resolution profile. In addition, in the medium to high SNR region, the ADC resolutions have a more significant effect on the rate compared to the number of antennas. Our work also reveals that the performance gap between the perfect and imperfect CSI cases is smaller for lower ADC resolutions, hence imperfect CSI is better tolerated at lower resolutions.

We study the performance of generalized user-relay selection (GURS) scheme in network-coded cooperation systems. In particular, we propose the most general case of user-relay selection mechanism that selects any arbitrary subsets of users and relays subject to any practical constraints such as load balancing conditions, scheduling policy, and other factors. Our results thus can be applied to a large set of situations and include all existing results in the literature as special cases. We develop performance characterizations of the system under consideration in terms of outage probability over non-identically and independently distributed (n.i.i.d.) Rayleigh fading channels. The asymptotic outage expressions at high signal-to-noise ratio (SNR) regime are further derived and then, based on the derived expressions, we quantify the diversity order. The theoretical derivations are validated through Monte-Carlo simulations.

This paper considers a multiple-input multiple-output (MIMO) multi-way relay network (MWRN) where users exchange their information via a multi-way relay equipped with a large-scale antenna array, i.e., massive MIMO multi-way relay. Further, each antenna at the relay station is assumed to have a pair of low-resolution analog-to-digital converters (ADCs) to reduce the energy consumption and hardware cost at the relay. Lloyd-max algorithm is used to find the mean-squared error (MSE) optimum quantization labels and thresholds for the ADCs. With perfect channel state information (CSI) and zero-forcing (ZF) beam-forming for both reception and transmission at the relay, a closed-form approximation for the average achievable rate of each pair of users is derived with the help of Bussgang's decomposition. The results enable us to understand the achievable rate behavior with respect to system parameters, and especially to quantify the performance degradation caused by low-resolution ADCs. Numerical results verify the validity of Bussgang's theorem in our case, and that the derived result is an accurate performance predictor of the network. Further, both analytical and theoretical results reveal that the effect of ADC resolutions on the rate performance is as significant as the relay and users' transmit powers.

We propose a novel transmission protocol for multiway relay networks (MWRNs) in which the number of timeslots required for full mutual multi-way data exchange among K user nodes can be reduced to just two from Γ(K - 1)/21 + 1 in the current state-of-the-art. The proposed MWRN adopts superposition-coded transmission, successive interference cancellation (SIC) reception, power-domain non-orthogonal multipleaccess (NOMA) and linear detection/precoding facilitated by massive multiple-input multiple-output (MIMO). First, the user nodes transmit their signals to a massive MIMO-enabled relay, where a linear detector based on maximal ratio combining criterion is used for signal reception. Next, the relay composes a superposition-coded signal for each user node and transmits towards the user nodes by using a linear precoder based on maximal ratio transmission criterion. User nodes perform SICbased decoding for retrieving symbols sent by the remaining K user nodes. Thus, our proposed MWRN protocol completes the full mutual multi-way data exchange among all users within two time-slots. We derive the achievable sum rate of it via the so-called worst-case Gaussian approximation and show that a significant spectral efficiency gain can be achieved over the existing MWRN counterparts.

In this paper, we study the performance of opportunistic source selection (OSS) in multisource multirelay network-coded cooperative (NCC) systems. For this system, we derive the exact outage probability and asymptotic measures such as the diversity and coding gains. The derived analytical results provide an efficient means to evaluate the impact of different system parameters on the system performance. Our results reveal that the proposed NCC system greatly exploits the diversity gains in multisource multirelay NCC systems and thus provides a considerable performance improvement. From the derived closed-form diversity gains, we also evaluate the optimal number of selected relays that maximizes the achievable diversity gain. Numerical results are also presented to validate the theoretical analysis.

In an Internet of Things (IoT) network, heterogeneous users with different priorities and service requirements will co-exist. This makes scheduling access to the shared communication medium a major challenge. To tackle this challenge, we consider the application of irregular repetition slotted ALOHA (IRSA), one of the best-performing random access protocols for homogeneous networks, for a heterogeneous multiclass IoT network. To this end, centralized and distributed implementations of the IRSA for multiclass IoT networks is proposed. Then, we focus on finding the network performance boundaries by studying the set of feasible throughput values for each class achieved via IRSA, called the capacity region. In addition to identifying the capacity region, the average and maximum delay of the users' packet delivery for both centralized and distributed IRSA are investigated. Our throughput and delay analysis reveals that the performance of distributed IRSA achieves that for the centralized implementation as the number of users increases. Further, we use our capacity region analysis to find the optimal IRSA strategy that maximizes the weighted sum-throughput of the network.

We consider the use of deep neural network (DNN) to develop a decision-directed (DD)-channel estimation (CE) algorithm for multiple-input multiple-output (MIMO)-space-time block coded systems in highly dynamic vehicular environments. We propose the use of DNN for k -step channel prediction for space-time block code (STBC), and show that deep learning (DL)-based DD-CE can remove the need for Doppler rate estimation in fast time-varying quasi stationary channels, where the Doppler rate varies from one packet to another. Doppler rate estimation in this kind of vehicular channels is remarkably challenging and requires a large number of pilots and preambles, leading to lower power and spectral efficiency. We train two DNNs which learn the real and imaginary parts of the MIMO fading channels over a wide range of Doppler rates. We demonstrate that by these DNNs, DD-CE can be realized with only priori knowledge about Doppler rate range and not the exact value. For the proposed DD-CE algorithm, we also analytically derive the maximum likelihood (ML) decoding algorithm for STBC transmission. The proposed DL-based DD-CE is a promising solution for reliable communication over vehicular MIMO fading channels without accurate mathematical models. This is because DNNs can intelligently learn the statistics of the fading channels. Our simulation results show that the proposed DL-based DD-CE algorithm exhibits lower error propagation compared to existing DD-CE algorithms which require perfect knowledge of the Doppler rate.

The successive-cancellation list (SCL) and successive-cancellation flip (SCF) decoding can be used to improve the performance of polar codes, especially for short to moderate length codes. However, their serial decoding nature results in significant decoding latencies. Implementing some operations in parallel can reduce their decoding latencies. This paper presents fast implementations of the SCL and SCF decoders. In particular, we propose fast parallel list decoders for five newly identified types of nodes in the decoding tree of a polar code, which significantly improves the decoding latency. We also present novel fast SCF decoders that decode some special nodes in the decoding tree of a polar code without serially computing bit log-likelihood ratios. Using our proposed fast parallel SCF decoders, we observed an improvement up to 81% with respect to the original SCF decoder. This significant reduction in the decoding latency is observed without sacrificing the bit-error-rate performance of the code.

Network-coded cooperation (NCC) has recently gained interest as it improves the network throughput in multi-source cooperative systems. NCC has been studied for single-antenna terminals only. Employing multiple-input multiple-output (MIMO) techniques can significantly improve the performance of NCC systems. Furthermore, the existing relay selection (RS) strategies for NCC utilize the “max-min” end-to-end (E2E) criterion. This selection strategy (called Strategy A) is complicated even for a network with single-antenna terminals as it requires global channel state information (CSI). This requirement makes it hard to implement RS-based NCC. To counter this issue, we introduce a new RS strategy (Strategy B), which utilizes only the local CSI (not global CSI), significantly reducing the signaling overhead without sacrificing the performance. The performance of MIMO-NCC under Strategies A and B is studied over independent and non-identically distributed (i.n.i.d.) Rayleigh fading channels. Relays and the destination are equipped with multiple antennas, whereas sources have a single antenna. The exact outage probability expressions of the system under consideration are derived. The asymptotic outage expressions are further provided to obtain valuable insights into the practical system-design parameters such as the diversity order and coding gain. Furthermore, numerical results are provided in support of the analytical results.

In this paper, a deep learning (DL)-based sphere decoding algorithm is proposed, where the radius of the decoding hypersphere is learned by a deep neural network (DNN). The performance achieved by the proposed algorithm is very close to the optimal maximum likelihood decoding (MLD) over a wide range of signal-to-noise ratios (SNRs), while the computational complexity, compared to existing sphere decoding variants, is significantly reduced. This improvement is attributed to the DNN's ability of intelligently learning the radius of the hypersphere used in decoding. The expected complexity of the proposed DL-based algorithm is analytically derived and compared with existing ones. It is shown that the number of lattice points inside the decoding hypersphere drastically reduces in the DL-based algorithm in both the average and worst-case senses. The effectiveness of the proposed algorithm is shown through the simulation for high-dimensional multiple-input multiple-output (MIMO) systems, using high-order modulations.

This paper proposes a novel lower bound on the Bhattacharyya parameter of synthesized channels in polar codes. The proposed bound is a result of a newly defined merge operation that reduces the cardinality of output alphabets of a symmetric binary-input discrete memoryless channel. By repeated applications of the proposed merge operation, we establish a universal bound on the Bhattacharyya parameters of synthesized channels that holds for any symmetric binary-input discrete memoryless transmission channel. We then discuss some applications of the new bound. For example, using the derived universal lower bound along with the existing upper bound, we find a partial order among the Bhattacharyya parameters of those synthesized channels that cannot be ordered through existing results. This ordering can help efficient design of polar codes. In addition, some extremal behaviors of the binary-symmetric channel are also proved.

Locally repairable codes (LRCs) have been recently proposed and used in real-world distributed storage systems (DSSs) such as Microsoft Azure Storage and Facebook HDFS-RAID (Hadoop Distributed File System-Redundant Array of Independent Disks). Since information in DSSs is changed frequently, reducing update complexity (UC) of LRCs is of great interest. In this paper, we propose code design algorithms that can reduce UC of existing LRCs without sacrificing their important code parameters such as minimum distance, code rate, or locality. We establish bounds on UC, and use them to show that our algorithms can achieve optimal or near optimal UC for a large class of LRCs.

The ever increasing demands for mobile network access have resulted in a significant increase in bandwidth usage. By improving the system spectral efficiency, multi-way relay networks (MWRNs) provide promising approaches to address this challenge. In this paper, we propose a novel linear beamforming design, namely partial zero-forcing (PZF), for MWRNs with a multiple-input-multiple-output relay. Compared to zero-forcing (ZF), PZF relaxes the constraints on the relay beamforming matrix such that only partial user-interference, instead of all, is canceled at the relay. The users eliminate the remaining interferences through self-interference and successive interference cancellation. A sum-rate maximization problem is formulated and solved to exploit the extra degrees-of-freedom resulted from PZF. Simulation results show that the proposed PZF relay beamforming design achieves significantly higher network sum-rates than the existing linear beamforming designs.

A linear block code with dimension k, length n, and minimum distance d is called a locally repairable code (LRC) with locality r, if it can retrieve any coded symbol by at most r other coded symbols. LRCs have been recently proposed and used in practice in distributed storage systems, such as Windows Azure Storage and Facebook HDFS-RAID. Theoretical bounds on the maximum locality of LRCs (r) have been established. The average locality of an LRC (r) directly affects the costly repair bandwidth, disk I/O, and the number of nodes involved in the repair process of a missing data block. There is a gap in the literature studying r. In this paper, we establish a lower bound on r of arbitrary (n, k, d) LRCs. Furthermore, we obtain a tight lower bound on r for a practical case where the code rate (R = (k/n)) is greater than (1 - (1/√n))2. Finally, we design three classes of LRCs that achieve the obtained bounds on r. Comparing with the existing LRCs, our proposed codes improve the average locality without sacrificing such crucial parameters as the code rate or minimum distance.

Instantly decodable network codes (IDNCs) are suggested in the literature to mitigate the problem of decoding delay in network coding. IDNC is also suggested for broadcast scenarios, where the goal is to maximize the number of decoded packets by the receivers, e.g., in multimedia broadcast. It is shown that after uncoded transmission of all the packets, one coded packet can be instantly decodable by a large number of users, when the transmitter is sighted, i.e., it has a perfect knowledge of the lost packets by each receiver. We introduce and study blind IDNC for broadcast, where the transmitter has no knowledge of the lost packets. Similar to the sighted IDNC, first all data packets are transmitted uncoded. Then, assuming the same erasure rate for all users, we allow a small number of coded packets (one, two or three), and study how these coded packets should be constructed to recover as many lost packets at the receivers as possible. The optimal solutions when one blind packet or two non-overlapping blind packets are transmitted are found. We see that two blind transmissions have comparable performance to a single optimal sighted transmission. Moreover, we prove that three blind transmissions outperform any single sighted transmission.

Distributed storage systems (DSSs) provide a scalable solution for reliably storing massive amounts of data coming from various sources. Heterogeneity of these data sources often means different data classes (types) exist in a DSS, each needing a different level of quality of service (QoS). As a result, efficient data storage and retrieval processes that satisfy various QoS requirements are needed. This paper studies storage allocation, meaning how the data of different classes is spread over storage nodes, for a multi-class DSS. More specifically, assuming a probabilistic access to the storage nodes, we aim at maximizing the weighted sum of the probability of successful data recovery of data classes, when for each class a minimum QoS (probability of successful recovery) is guaranteed. Solving this optimization problem for a general setup is intractable. Thus, we find the optimal storage allocation when the data of each class is spread minimally over the nodes, i.e. minimal spreading allocation (MSA). Then, by comparing the performance of the optimal MSA with the performance upper bound, we show that the optimal MSA is indeed the optimal storage allocation in many practical cases. Numerical examples are also presented for better illustration of the results.

Locally repairable codes (LRCs) have been proposed and used in practice as effective coding methods for distributed storage systems (DSSs). In a DSS, information block recovery is a critical task performed in the case of data node permanent failure or temporal unavailability. Temporal node unavailability accounts for 90% of all block recoveries triggered in DSS. Since parity blocks are not needed to be recovered during a temporal node unavailability, special attention should be given to reconstruction of information blocks when trying to minimize the average bandwidth needed for block recovery. Motivated by this, in this work, we study the average locality ofinformation blocks. We obtain a lower bound on the average locality of information blocks of LRCs and design LRCs that achieve the bound. In addition to obtaining the optimal average locality for the information blocks, our codes achieve the optimal maximum locality for all the information blocks as well as some parity blocks (in some cases all the parity blocks).

Network coded cooperation (NCC) has recently gained interest due to its ability to increase the network throughput in multisource cooperative systems. NCC with single relay selection (SRS) or multiple relay selection (MRS) has been studied for single-antenna terminals only. Employing multiple-input multiple-output (MIMO) can significantly improve the performance of NCC systems. In this paper, we consider a NCC system with decode-and-forward (DF) relaying where relays use maximum distance separable (MDS) codes as their encoding vectors. More specifically, we consider N sources, M relays and a single destination. Relays and the destination are equipped with multiple antennas whereas sources have single antenna. The performance of the system under consideration is investigated by deriving exact outage probability expressions for both SRS and MRS protocols. The asymptotical diversity orders are further provided to obtain valuable insights into practical system design. Furthermore, numerical results are provided to validate the accuracy of our derivations and quantify the effect of system parameters on the outage probability and diversity order.

In this paper, we investigate the performance of network coded cooperation (NCC) systems based on relay selection in the presence of imperfect channel state information (CSI). Specifically, we consider an uplink cellular scenario with N sources, M relays and a single destination. The relays adopt decode and forward (DF) relaying and use maximum distance separable (MDS) codes as their encoding vectors. We investigate the impact of imperfect CSI on outage probability and asymptotic and finite-SNR diversity-multiplexing tradeoff (DMT) of the system under consideration. Simulation results are further presented to corroborate the analytical findings and provide insight into the system design where imperfect CSI and finite SNR regime are taken into account.

Erasure codes are recently used in real-world distributed storage systems (DSSs) such as Google File System,Microsoft Azure Storage, and Facebook HDFS-RAID for data reliability. When designing erasure codes for DSSs, special attention is given to the associated costs of data handling operations such as repair or update. For example, locally repairable codes (LRC) are designed and used in DSSs to allow for low-cost repair of failed blocks. Update complexity (defined as the number of blocks that need to be updated when an information block is changed) is yet another design parameter. This parameter can be seen as a measure of the computation, I/O and networking costs associated with updating an information block in a DSS. Since information is frequently updated by many applications, lowering update complexity can result in lower power consumptions in DSSs. In this work, we study the update complexity of LRCs. Based on our study, we propose an improvement over the LRC used by Facebook HDFS-RAID. Keeping the same code parameters including length, storage overhead, minimum distance and cost of repair (locality), we improve the update complexity by more than 16%. Moreover, we show that with these parameters achieving a lower update complexity is impossible.

We analyze relay selection for an underlay cognitive radio (CR) two-way relay network (TWRN) with zero-forcing (ZF) transmission and receiving. The source and the destination nodes are massive multiple-input multiple-output (MIMO) enabled. Relays will perform amplify and forwarding (AF) while the destination and source nodes perform self interference cancellation. We first obtain asymptotic signal-to-interference-plus-noise ratio (SINR) values under the power scaling at the relay and end nodes. Then, we derive optimal power allocation schemes for the end nodes to satisfy the interference constraints at the primary user (PU). Based on these optimal values, we analyze the effect of relay selection on the sum rate. With the use of massive MIMO, the SINR and the sum rate will only depend on the pathloss coefficients of the channels and average noise levels. Thus, the relay selection can be done at the deployment stages of the system and most of the time it simplifies to selection of the relay with the highest number of antennas. Our simulation results validate the analytical asymptotic results and qualify CR massive MIMO TWRNs as a possible candidate for future wireless systems.

This paper analyzes the problem of optimum user association and sum rate maximization for software defined radio access networks (SD-RANs) with access node diversity for fifth generation (5G) wireless networks. We consider four complementary types of access nodes namely, a massive multiple- input multiple-output (MIMO) base station (BS), MIMO BSs, small cells (SCs), and indoor and outdoor distributed antenna systems (DAS). The SDRAN user association problem is solved through a novel three-stage optimization scheme called the place coverage (TPC). TPC divides the user equipment (UEs) into two sets of indoor and outdoor UEs. Initially, TPC associates indoor UEs with the indoor DAS access nodes. Next, outdoor UEs are associated with the outdoor DAS access nodes, SCs, MIMO BSs, and the massive MIMO BS. Finally, the remaining resources of indoor and outdoor access nodes are used to serve the UEs that have not been served. The scope of TPC is multifold. First, TPC reflects the closest model to a real-world diverse 5G network. Secondly, servicing the indoor UEs with iDAS antennas results in lower power load per user for the access network resulting in better coverage, quality, and data speed. Thirdly, TPC provides reduced radiation levels for indoor UEs. Numerical results show that TPC provides significant sum rate and fairness gains over the received signals strength (RSS) based association schemes [1]. Moreover, TPC provides comparable performance levels as the optimum association scheme based on exhaustive search while bringing significant complexity reduction.

The authors study the transmit power allocation (PA) problem for a network of two multi‐antenna terminals (one of which is a massive multiple‐input and multiple‐output (MIMO) terminal) and a two‐way, amplify‐and‐forward relay. The relay is limited to a single antenna. Using perfect channel state information, the terminals employ beamforming with maximum‐ratio‐transmission and maximum‐ratio‐combining for transmission and reception, respectively. The authors investigate two practical problems, namely; (i) maximising the sum rate subject to a total power constraint (ii) maximising the sum rate when one of the terminals must exceed a target signal‐to‐noise ratio (SNR). For the first case, the authors derive the closed‐form optimal PA and for the second, the authors derive a sub‐optimal PA. In both cases, the resulting sum rates are a function of instantaneous channel gains. Thus by averaging over the Nakagami‐ m distribution and exploiting the weak law of large numbers, the authors derive the closed‐form ergodic sum rates. Finally, the simulation results validate the theoretical analysis and show the sum‐rate improvements over uniform PA. For example, to achieve 4 bit/s/Hz, a uniform allocation needs 1 dB more than the authors’ optimal allocation. When one of the SNRs must exceed a target value, the gap between the authors’ sub‐optimal PA and random PA increases to 2 dB.

In a multiway relay channel (MWRC), pairwise transmission strategy can be used to reduce the computational complexity at the relay and the users without sacrificing the data rate significantly. The performance of such pairwise strategies, however, is affected by the way that the users are paired to transmit. In this paper, we study the effect of pairing on the common rate and sum rate of an MWRC with functional-decode-forward (FDF) relaying strategy where users experience asymmetric channel conditions. To this end, we first develop a graphical model for an MWRC with pairwise transmission strategy. Using this model, we then find the maximum achievable common rate and sum rate as well as the user pairings that achieve these rates. This marks the ultimate performance of FDF relaying in an MWRC setup. Further, we show that the rate enhancement achieved through the optimal user pairing becomes less pronounced at higher signal to noise ratios. Using computer simulations, the performance of the optimal pairing is compared with those of other proposed pairings in the literature.

We study the video recommendation problem based on a large amount of user viewing logs instead of explicit ratings. As viewing records are implicitly suggest user preferences, existing matrix factorization methods fail to generate discriminative recommendations based on such one-class positive samples. We propose a scalable approach called separating-plane matrix factorization (SPMF) to make effective recommendations based on positive implicit feedback, with a learning complexity that is comparable to traditional matrix factorization. With extensive offline evaluation in Tencent Data Warehouse (TDW) based on a large amount of data, we show that our approach outperforms a wide range of state-of-the-art methods. We also deployed our system in the QQ Browser App of Tencent and performed online A/B testing with real users. Results suggest that our approach increased the video click through rate by $23% over implicit-feedback collaborative filtering (IFCF), a scheme available in Apache Spark's MLlib.

This paper investigates the impact of co-channel interference (CCI), imperfect channel state information (CSI) and pilot contamination for multi-pair massive multiple-input multiple-output (MIMO) two-way relay networks (TWRNs). We consider a multi-cell TWRN system consisting of single-antenna user nodes and amplify-and-forward (AF) relay nodes having very large antenna arrays. Under the aforementioned channel imperfections, the asymptotic signal-to-interference-noise ratio and asymptotic sum rate expressions are derived in closed-form whenever the number of relay antennas grows unbounded with respect to the number of user nodes. For perfect CSI case, the transmit power at the user nodes and the relay can be scaled down inversely proportional to the number of antennas at the relay. Moreover, for the imperfect CSI case, these transmit powers can only be scaled down inversely proportional to the square-root of the relay antenna count. Thus, even with imperfect CSI, the benefits of employing a massive MIMO-enabled relay on transmit power savings are significant. Moreover, our analysis shows that although the detrimental effect of CCI can be asymptotically negated completely, the residual interference due to pilot contamination cannot be mitigated even in the limit of infinitely many relay antennas.

Storage allocation affects important performance measures of distributed storage systems. Most previous studies on the storage allocation consider its effect separately either on the success of the data recovery or on the service rate (time) where it is assumed that no access failure happens in the system. In this paper, we go one step further and incorporate the access model and the success of data recovery into the service rate analysis. In particular, we focus on quasi-uniform storage allocation and provide a service rate analysis for both fixed-size and probabilistic access models at the nodes. Using this analysis, we then show that for the case of exponential waiting time distribution at individuals storage nodes, minimal spreading allocation results in the highest system service rate for both access models. This means that for a given storage budget, replication provides a better service rate than a coded storage solution.

Erasure codes, such as LT and Raptor codes, are designed for the purpose of erasure-resilient distribution of data over computer networks. To achieve a small reception overhead, however, LT and Raptor codes must be used with a large design length$k$, making these codes unsuitable for real-time applications. In this paper, we propose a new class of erasure codes based on Reed–Solomon codes that unlike other Reed–Solomon-based erasure codes are rateless and also, unlike other rateless codes, guarantee zero overhead even for small$k$. Moreover, they have a reasonable computational complexity of coding when$k$is not too large. In fact, a practical implementation of subfield subcodes of Reed-Solomon codes with arbitrarily large block lengths is presented.

An (n, k) erasure code that can recover any coded symbol by at most r other coded symbols is called a locally repairable code (LRC) with locality r. LRCs have been recently implemented in distributed storage systems. Coding complexity reduction can be significantly decreased by using binary LRCs (BLRCs) as they eliminate costly multiplication calculation. In this paper, motivated by the recently erasure codes with d = 4 used in practice, we propose BLRCs when (r + 1) | n and d = 4. We prove that our proposed binary codes are optimal for r ∈ {1, 3}, meaning that neither their locality nor their minimum distance can be improved by non-binary codes. For r ≥ 4, our proposed binary codes offer near-optimal code rate, with a rate gap of O(log r/n) compared with optimal nonbinary codes. While keeping the bulk of code structure binary, we eliminate this rate gap by using fields with sizes as small as r + 2 for only two redundant symbols. These non-binary codes still eliminate the need for costly multiplications in many operations including a single failure repair (a dominant repair scenario). Using the construction of spanning BLRC with d = 4 as a backbone, we also construct LRCs with minimum distance d ≥ 6. Furthermore, we obtain a closed-form equation for the mean-time to data-loss of arbitrary erasure codes.

Multi-way relaying is a cooperative scheme for communication scenarios where several users want to share their data with each other. While the capacity of multi-way relay channels (MWRCs) is still unknown to completely understand their potentials, the achievable data rates of MWRCs have been studied for specific setups. In this work, we aim to get a better understanding of the achievable data rates of an amplify-and-forward (AF) MWRC. To this end, we first present an achievable upper bound for the common data rate of an AF MWRC and discuss how users' power allocation affects the common rate. While full power transmission at the users assures reaching the maximum achievable common rate in one-way relaying, we show that it is not the case for MWRCs. Thus, we formulate an optimization problem to find the optimal users' power allocation to gain the maximum common rate. Finding an optimal solution for this optimization problem is quite complex since the number of constraints grows exponentially with the number of users. We then focus on a relaxed version of the rate optimization problem and propose a suboptimal algorithm to solve it. Our simulation results show that the proposed algorithm can achieve rates higher than the ones achieved through full power transmission with noticeably lower transmit power at the users.

Relay selection strategies help to improve spectral and energy efficiencies, to enhance transmission robustness, or to reduce latency in multi-relay cooperative networks. Two novel relay selection strategies are proposed and analyzed here for multiple-input multiple-output (MIMO) amplify-and-forward (AF) two-way relay networks (TWRNs) with spatial multiplexing. Specifically, they are designed to maximize the effective end-to-end signal-to-noise ratio (SNR), and thereby minimize the overall outage probability or maximize the achievable sum rate. Interestingly, the first strategy amounts to maximizing the minimum of the eigenvalues of the Wishart matrices from the selected relay to the two user nodes. Counter-intuitively, the latter strategy amounts to maximizing the minimum of the determinant of the same Wishart matrices. The performance of these two strategies is investigated by deriving lower/upper bounds of the overall outage probability and the average sum rate approximations in closed form. Further, the asymptotic high-SNR approximations of the outage probability are derived, and thereby, the achievable diversity-multiplexing tradeoff is quantified. This tradeoff reveals that whenever the sum of relay antennas is fixed, the achievable diversity order is always a constant, and hence, the multiplexing gain can indeed be improved by equally distributing antennas among the available set of relays. Our results reveal that relay selection indeed significantly alleviates the inherent diversity-gain loss associated with the use of available degrees of freedom for spatial multiplexing.

In this paper, we study the effect of users' transmission ordering on the common rate and sum rate of pairwise multiway relay channels (MWRCs) with functional-decode-forward strategy. To this end, we first develop a graphical model for the data transmission in a pairwise MWRC. Using this model, we then find the optimal orderings that achieve the maximum common rate and sum rate of the system, respectively. The achieved maximum common/sum rate is also found. Moreover, we show that the performance gap between optimal orderings and a random ordering vanishes when SNR increases. Computer simulations are presented for better illustration of the results.

Amplify-and-forward (AF) and demodulate-and-forward (DMF) can be effectively used in memoryless two-way relay channels (TWRCs) to enhance the spectral efficiency. In this paper, we study AF and DMF, in terms of their achievable data exchange rate, for a memoryless TWRC. Our results show that unlike memoryless one-way relaying, increasing users' SNR benefits AF more than DMF. Another interesting observation is that while with DMF a higher data rate is provided for the user whose channel condition is better, with AF the situation is the reverse. That is, the user with worse channel condition can receive at a higher data rate. Further, we find that for a TWRC with asymmetric users' channels, AF can take advantage of power back-off at the users, without degrading the data rate, to improve the energy efficiency while power back-off is not beneficial for DMF.

Two transmission strategies, namely (i) pairwise zero-forcing transmission and (ii) non-pairwise zero-forcing transmission, for multiple-input multiple-output (MIMO) amplify-and-forward (AF) multi-way relay networks (MWRNs) are analytically studied. To this end, lower and upper bounds of the outage probability, the corresponding high signal-to-noise ratio outage probability approximations, the achievable sum rate, and the fundamental diversity-multiplexing trade-off are derived in closed-form. The proposed pairwise zero-forcing transmission strategy possesses a lower practical implementation complexity as each node requires only the instantaneous respective node-to-relay channel knowledge. Counter intuitively, the non-pairwise zero-forcing transmission strategy achieves higher spatial multiplexing gains over the pairwise counterpart at the expense of higher relay processing complexity and more stringent channel state information requirements. Moreover, numerical results are presented to further validate our analysis and thereby to obtain valuable insights into practical MIMO AF MWRN implementation.

We consider an erasure multi-way relay channel (EMWRC) in which several users share their data through a relay over erasure links. Assuming no feedback channel between the users and the relay, we first identify the challenges for designing a data sharing scheme over an EMWRC. Then, to overcome these challenges, we propose practical low-latency and low-complexity data sharing schemes based on fountain coding. Later, we introduce the notion of end-to-end erasure rate (EEER) and analytically derive it for the proposed schemes. EEER is then used to calculate the achievable rate and transmission overhead of the proposed schemes. Using EEER and computer simulations, the achievable rates and transmission overhead of our proposed schemes are compared with the ones of one-way relaying. This comparison implies that when the number of users and the channel erasure rates are not large, our proposed schemes outperform one-way relaying. We also find an upper bound on the achievable rates of EMWRC and observe that depending on the number of users and channel erasure rates, our proposed solutions can perform very close to this bound.

The i.i.d. duplication channel which duplicates each symbol independently with a certain probability is studied. The contribution is twofold: first, a tight lower bound on the capacity of such channels is introduced. Second, the capacity is computed for the small values of the duplication probability using a series expansion representation.

The sum rate of multiple-input multiple-output (MIMO) amplify-and-forward (AF) two-way relay networks (TWRNs) with zero-forcing (ZF) transmission is analyzed. Namely, (1) ZF at the two sources for transmission and reception and (2) ZF at the relay for transmission and reception, are treated. Specifically, the exact sum rate expressions and corresponding high signal-to-noise ratio (SNR) approximations are derived for uncorrelated and min-semi-correlated (i.e., correlation exists only at the minimum antenna terminal) Rayleigh fading cases in closed-form. Moreover, the closed-form upper and lower bounds of the sum rate are derived for max-semi-correlated (i.e., correlation exists only at the maximum antenna terminal) and doubly-correlated Rayleigh fading cases. Notably, these sum rate bounds and high SNR approximations provide valuable insights into practical MIMO AF TWRN system-design and the maximum achievable spatial multiplexing gain. All the analyses are verified by using Monte-Carlo simulations.

The sum rate of multiple-input multiple-output (MIMO) amplify-and-forward (AF) two-way relay networks (TWRNs) with transmit/receive zero-forcing (ZF) is analytically studied. Specifically, the exact sum rate expressions are derived for uncorrelated and semi-correlated Rayleigh fading cases in closed-form. Moreover, the closed-form upper and lower bounds of the sum rate are derived for doubly-correlated Rayleigh fading. In particular, these sum rate bounds are tight, and consequently, serve as benchmarks providing valuable insights into practical MIMO AF TWRN system-design. All the analyses are verified by using Monte-Carlo simulations.

A pair-wise transmit/receive zero-forcing (Tx/Rx ZF) transmission strategy is proposed and analyzed for multiple-input multiple-output (MIMO) amplify-and-forward (AF) multi-way relay networks (MWRNs). The performance of this system set-up is studied by deriving lower and upper bounds of the overall outage probability, the corresponding high signal-to-noise ratio outage approximations, and the achievable diversity-multiplexing trade-off. The proposed pair-wise Tx/Rx ZF transmission strategy possesses a lower implementation complexity as each source requires only the instantaneous respective source-to-relay channel knowledge. Moreover, our analysis provides valuable insights into practical MIMO AF MWRN implementation.

A novel joint beamforming and antenna selection strategy is proposed and analyzed for two-way multiple-input multiple-output amplify-and-forward relay networks. Specifically, this strategy selects the optimal transmit precoding and receiver filtering vectors at the two source terminals, and an optimal transmit/receive antenna at the relay terminal based on minimizing the overall outage probability. The performance of this transmission strategy is quantified by first deriving the exact cumulative distribution function of the effective signal-to-noise ratio (SNR), and thereby, evaluating the overall outage probability, its asymptotically exact high SNR approximation and achievable diversity order. For a multiple relay scenario, a joint relay, beamforming, and antenna selection strategy is proposed and analyzed as well. Interestingly, our selection strategies are optimal in the sense of the overall outage probability, and hence, in the sense of achievable diversity order as well.

Multi-way relaying is a promising approach to enhance the spectral efficiency in multi-user communication systems. Several relaying strategies have been proposed recently to be used in multi-user communication systems. In this paper, we analyze the gap between the achievable rate of some of these relaying techniques and the capacity of the Gaussian multiway relay channels (GMWRCs). To this end, for a symmetric GMWRC with K users, we prove that lattice-based relaying guarantees a gap less than 1/2(K-1) bit from the capacity upper bound. Also, we show that decode-and-forward and amplify-and-forward relaying may have a larger capacity gap than 1/2(K-1) bit depending on the relay and users' SNR. Then, we find the SNR regions where these two techniques also ensure a 1/2(K-1)-bit gap.

Two new transmit/receive (Tx/Rx) antenna selection strategies are proposed and analyzed for two-way multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay networks. These two strategies select the best transmit and receive antennas at the two sources and the relay based on (i) minimizing the overall outage probability and (ii) maximizing the sum-rate. The performance of these selection strategies is quantified by deriving the overall outage probability, its high SNR approximation and the diversity order providing valuable insights into practical system-designs. Importantly, multiple relay and multiple user two-way relay network set-ups are also treated by proposing and analyzing (i) joint relay and antenna selection strategies, and (ii) joint user, relay and antenna selection strategies, respectively. Interestingly, our outage probability results reveal that the joint relay and antenna selection strategies achieve significant diversity and array gains over those of their single relay counterparts. In fact, the diversity orders of individual relayed-branches accumulate to yield the overall diversity of the multi-relay networks. For example, at 10-2outage probability, the dual-antenna relay provides a 14 dB gain over a single-antenna relay, and having two dual-antenna relays improves the gain by another 5 dB. Moreover, the performance degradation due to practical transmission impairments (i) feedback delays, (ii) spatially-correlated fading and (iii) non-identically distributed fading is quantified. Impact of channel prediction to circumvent outdated channel state information for antenna selection due to feedback delay is also studied. All the derivations are validated through Monte-Carlo simulations.

A comprehensive performance analysis framework for dual-hop multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay networks with hop-by-hop beamforming (i.e. both source and relay perform beamforming) is presented. The system performance degradation due to practical transmission impairments (i) feedback delays, (ii) channel estimation errors and (iii) spatially-correlated fading is quantified. To this end, closed-form expressions for the cumulative distribution function of the end-to-end signal-to-noise ratio, its moment generating function, the outage probability, and the average bit error rate (BER) are derived. The asymptotic high SNR approximations of the outage probability and average BER are derived to obtain valuable system-design insights such as the diversity order and array gain. In order to illustrate the usefulness of our analysis, four applications, which employ dual-hop MIMO relaying with hop-by-hop beamforming, are also presented and analyzed. Furthermore, our analyses are validated through Monte-Carlo simulations.

A wireless relay network with one source, one relay and one destination is considered, where nodes communicate via N orthogonal channels. We develop optimal power allocation strategies at both the source and relay for maximizing the overall source-destination capacity under individual power constraints at the source and relay. Some properties of the optimal solution are studied.

Based on a new vision of the inactivation decoding process, we set a new degree distribution design criterion for the LT part of Raptor codes. Under an infinite block length assumption, a family of degree distributions that satisfy the new design criterion is analytically derived. The finite length performance of this family is investigated by using computer simulations and is shown to outperform the conventional design.

We consider the problem of reliable communication over non-binary insertion/deletion channels where symbols are randomly deleted from or inserted in the received sequence and all symbols are corrupted by additive white Gaussian noise. To this end, we utilize the inherent redundancy achievable in non-binary symbol sets by first expanding the symbol set and then allocating part of the bits associated with each symbol to watermark symbols. The watermark sequence, known at the receiver, is then used by a forward-backward algorithm to provide soft information for an outer code which decodes the transmitted sequence. Through numerical results and discussions, we evaluate the performance of the proposed solution and show that it leads to significant system ability to detect and correct insertions/deletions. We also provide estimates of the maximum achievable information rates of the system, compare them with the available bounds, and construct practical codes capable of approaching these limits.

Four joint relay and antenna selection strategies for dual-hop amplify-and-forward (AF) multiple-input multiple-output relay networks are studied. Two of them require full channel state information (CSI) whereas the other two require only partial CSI. The relays are either channel-assisted AF or fixed-gain AF type. The first joint selection strategy involves choosing the best relay and the best single transmit antennas at the source and the relay. The second strategy jointly involves choosing the best relay and the best single transmit/receive antenna pairs at the source-to-relay and relay-to-destination channels. Moreover, two partial selection strategies, which can be used when the global CSI is not available, are also proposed and analyzed. In order to quantify the system performance analytically, the exact outage probability of all selection strategies is derived in closed-form. Direct insights into the system-design are obtained by deriving the asymptotic outage probability, asymptotic average symbol error rate, diversity order and array gain.

The resource allocation problem for two sources communicating via an amplify-forward relay is studied from an outage perspective. Analog network coding is considered for half-duplex nodes with perfect receiver-side channel knowledge. Under a sum power constraint, an optimal power allocation that minimizes an approximate outage probability is derived and shown to improve the performance upto 4.77 dB. A cut-set bound is also optimized to serve as a comparison reference. When such a power allocation is not feasible, two novel resource- optimized schemes, which exploit conventional one-way relaying, are proposed to reduce the outage at low multiplexing gains1.

In a system employing physical-layer network coding, the superimposed constellation at the relay may have ambiguity where one received signal is associated with more than one possible combination of users' data. We find the necessary and sufficient condition on a user bit mapping which removes this ambiguity for phase shift keying modulation. Further, we introduce the concept of semi-Gray mapping which improves the system BER performance and achievable rate. The necessary and sufficient condition of having a semi-Gray mapping is also found. Interestingly, the widely used binary reflected Gray mapping does not satisfy the semi-Gray mapping condition resulting in a poorer performance compared to our proposed semi-Gray scheme.

A novel transmit/receive (Tx/Rx) antenna selection strategy is proposed and analyzed for two-way multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay networks. This strategy involves choosing the best transmit and receive antennas at the two sources and the relay based on the minimization of the overall outage probability. The performance of the proposed selection strategy is quantified by deriving the overall outage probability and its high SNR approximation. Specifically, the diversity order is derived to obtain valuable insights into practical system designing. In particular, our results are extended to cater the multiple relay scenario, and thereby, a joint relay and Tx/Rx antenna selection strategy is proposed and analyzed. To this end, the overall outage probability, its high SNR approximation and diversity order are derived. Our numerical results show that the proposed selection strategies achieve the full diversity order. All the analyses are validated through Monte-Carlo simulations.

The estimation of an unknown parameter using distributed measurements is an essential problem in many wireless sensor network (WSN) applications. In a WSN, the shortage of resources, specially the energy in the sensors, acts as a constraint on the design of estimation algorithms. The existing studies on this problem have developed algorithms that try to limit the total energy in the whole network, yet not considering each sensor's energy consumption individually. We develop an estimation algorithm for inhomogeneous environments considering the transmission load of individual sensors.

A comprehensive performance analysis of dual-hop multiple-input multiple-output amplify-forward relay networks with hop-by-hop beamforming is presented. The impact of practical transmission impairments; (i) feedback delays, (ii) channel estimation errors and (iii) spatially-correlated fading on the system performance is studied. Specifically, the amount of performance degradation due to these impairments are quantified analytically and illustrated through numerical results. Numerical results show that these impairments degrade the system performance significantly. The cumulative distribution function of the end-to-end signal-to-noise ratio is derived and used to obtain the moment generating function, the outage probability, and the average symbol error rate (SER) in closed-form. The asymptotic outage probability and average SER are derived to obtain valuable system-design insights such as the diversity order and array gain. Further, our analyses are validated through Monte-Carlo simulations.

A novel approximation for the end-to-end signal-to-noise ratio (e2e SNR) of multi-hop (N≥2) fixed-gain amplify-and-forward (FG-AF) relay networks over independent and non-identically distributed Nakagami-m fading channels is proposed. Two types of FG-AF relays; (i) blind-AF, and (ii) semi-blind-AF are treated. The cumulative distribution and the moment generating function of the proposed e2e SNR approximation are derived in closed-form and used to derive the outage probability, the average symbol error rate, and the generalized SNR moments. The resulting performance metrics for the blind-AF relay case are asymptotically exact and thus, the asymptotic outage probability, the asymptotic average SER, the diversity order, and the coding gain are derived. Numerical and simulation results are presented to verify the comparative performance against the exact performance metrics and existing bounds. Our results reveal that the proposed performance approximations outperform the existing bounds in most of the cases.

In this paper, an extension of raptor codes is introduced which keeps all the desirable properties of raptor codes, including the linear complexity of encoding and decoding per information bit, unchanged. The new design, however, improves the performance in terms of the reception rate. Our simulations show a 10% reduction in the needed overhead at the benchmark block length of 64,520 bits and with the same complexity per information bit.

The power allocation problem corresponding to the communication of two sources via a relay with amplify-forward capability is studied from the outage probability perspective. Analog network coding is considered for half-duplex nodes with perfect channel state information at the receiver side. Under a sum-power constraint on the transmit powers of the nodes, an optimal power allocation strategy that minimizes the high signal-to-noise ratio approximation of the outage probability is derived and shown to improve the performance significantly. As a reference for comparison, a cut-set type bound is also optimized for the setup.

A new class of upper bounds on the end-to-end signal-to-noise ratio (SNR) of channel-assisted amplify-and-forward (AF) multi-hop (N ≥ 2) relay networks is presented. It is the half-harmonic mean of the minimum of the first P ≥ 0 hop SNRs and the minimum of the remaining N-P hop SNRs. The parameter P varies between 0 to N and may be chosen to provide the tightest bound. The closed-form cumulative distribution function and moment generating function are derived for independent and non-identically distributed Rayleigh fading and for independent and identically distributed Nakagami-m fading, where m is an integer. The resulting outage probability and the average symbol error rate bounds are asymptotically-exact. The asymptotic-exactness holds for any 0 ≤ P ≤ N. As applications, two cases of multi-hop multi-branch relay networks (i) the best branch selection and (ii) maximal ratio combining reception are treated. Numerical results are provided to verify the comparative performance against the existing bounds.

Log-likelihood ratio (LLR) computation for non-binary modulations over fading channels is complicated. A measure of LLR accuracy on asymmetric binary channels is introduced to facilitate good LLR approximations for non-binary modulations. Considering piecewise linear LLR approximations, we prove convexity of optimizing the coefficients according to this measure. For the optimized approximate LLRs, we report negligible performance loss compared to true LLRs.

Considering event-driven clustered wireless sensor networks, a probabilistic approach for analyzing the network lifetime is presented when events occur randomly over the network field. To this end, we first model the packet transmission rate of the sensors, using the theory of coverage processes and Voronoi tessellation. Then, the probability of achieving a given lifetime by individual sensors is found. This probability is then used to study the cluster lifetime. In fact, we find an accurate approximation for the probability of achieving a desired lifetime by a cluster. Our proposed analysis includes the effect of packet generation model, random deployment of sensors, dynamic cluster head assignment, data compression, and energy consumption model at the sensors. The analysis is presented for event-driven networks, but it comprises time-driven networks as a special case. Computer simulations are used to verify the results of our analysis.

Universal decentralized estimation (UDES) is one of the most well-known decentralized estimation techniques proposed for wireless sensor networks (WSNs). UDES and other decentralized estimation algorithms are proposed in view of the limited available energy at the sensors. In this work, we study energy efficiency of UDES for randomly deployed WSNs via finding the distribution and expected value of the number of bits that a sensor sends to the fusion center. Then, we find the probability of achieving a desired lifetime by the sensor. Our analytical results are verified through computer simulation.

In this paper, an analytical framework is developed for the performance analysis of three transmit antenna selection (TAS) strategies for dual-hop multiple-input multiple-output channel-assisted amplify-and-forward (CA-AF) relay networks over Rayleigh fading. The cumulative distribution function of a lower bound of the end-to-end signal-to-noise ratio (SNR) of the optimal TAS strategy is derived and used to obtain the upper bounds of the outage probability and the average symbol error rate (SER). The exact moment generating functions (MGFs) of the end-to-end SNR of two suboptimal TAS strategies are also derived for the ideal CA-AF MIMO relay networks. These MGFs are then used to present accurate and efficient closed-form approximations to evaluate the outage probability and average SER. Numerical and Monte-Carlo simulation results are provided to analyze the performance of the system and to verify the accuracy of our analytical framework.

In this paper, the effect of feedback delays on the performance of multiple-input multiple-output antenna amplify-and-forward relay networks with the best transmit/receive antenna pair selection over Rayleigh fading is studied. The cumulative distribution function and the moment generating function of the end-to-end signal-to-noise ratio (SNR) are derived. Closed-form expressions for the outage probability, average symbol error rate (SER), and the SNR moments are also derived. To gain further insights, the asymptotic outage probability, average SER, diversity order, and coding gain are presented. Numerical results and Monte-Carlo simulations are provided to illustrate the detrimental effects of feedback delays on the system performance and to verify the accuracy of our analysis.

The performance of a multi-hop amplify-and-forward relay network is analyzed. The source and destination terminals are equipped with multiple-antennas and the relays with single-antennas. The cumulative distribution function and the moment generating function of two tight upper bounds of the end-to-end signal-to-noise ratio are derived. The lower bounds for the outage probability and the average symbol error rate (SER) are also derived. The results take into account the source-relay and the relay-destination correlation matrices; the uncorrelated case is treated as well. The asymptotic outage probability, average SER, diversity order and coding gain are also derived. Numerical results and Monte-Carlo simulations are presented to analyze the system performance and show the tightness of the proposed bounds.

In this paper, we propose an output-threshold multiple relay selection scheme for dual-hop multi-branch cooperative wireless networks. The proposed scheme selects the first Lcarbitrary ordered relays out of L relays such that the maximal ratio combined signal-to-noise-ratio (SNR) of the Lcrelayed paths and the direct path barely exceeds a preset threshold. Closed-form expressions are derived for the cumulative distribution function, the probability density function, and the moment generating function of an output SNR upper bound for independent and identically distributed Rayleigh fading. Lower bounds for the outage probability, the average symbol error rate, and the average number of selected relays are also derived. Moreover, upper bounds for the average output SNR and the ergodic capacity are also derived. The analytical results are verified via the Monte-Carlo simulation. The performance of our proposed scheme is compared to that of the existing relay selection schemes. The proposed schemes provide more flexibility in utilizing bandwidth and spatial diversity in cooperative wireless networks.

This paper presents a new upper bound on the end-to- end signal-to-noise ratio (SNR) of channel-assisted amplify-and-forward (AF) multi-hop relay networks. The harmonic mean of the minimum of the first P ≥ 0 hop SNRs and the minimum of the remaining hop SNRs forms the new bound. Closed-form expressions are derived for the cumulative distribution function and the moment generating function of this SNR upper bound for independent and non-identically distributed Rayleigh, and independent and identically distributed Nakagami-m fading, where m is an integer. The outage probability and the average symbol error rate bounds are also derived. Our proposed bounds are compared against the existing bounds.

Receive antenna selection for unitary space-time modulation (USTM) over semi-correlated Ricean fading channels is analyzed (this work generalizes that of Ma and Tepedelenlio-glu for the independent and identically distributed (i.i.d.) Rayleigh fading case). The antenna selection rule is that the receive antennas with the largest signal powers are chosen. For single antenna selection, we derive the maximum likelihood decoding for the correlated Ricean case. We also derive the Chernoff bound on the pairwise error probability for the high signal to- noise ratio (SNR) region and obtain the coding gain and diversity order. Our results show that even when there are transmitter side correlations and a line of sight component, receive antenna selection with USTM preserves the full diversity order if the USTM constellation is of full rank. We also give an approximation to the distribution function of a quadratic form of non-zero mean complex Gaussian variates (from Nabar et al.) at the high SNR region. Based on this approximation, a closed-form expression for the coding gain is also obtained and compared with that of the i.i.d. Rayleigh case. We also analyze the case of multiple receive antenna selection and derive the coding gain and diversity order. We show that USTM constellations, which have been proposed for the i.i.d. Rayleigh channel, can be used with the correlated Ricean channel as well.

Irregular low-density parity-check (LDPC) code design for parallel sub-channels with different qualities is investigated. Such channels appear in many communication systems, e.g., orthogonal frequency-division multiplexing systems. When channel knowledge is available at both the transmitter and receiver, following the literature, we consider allotted LDPC codes which carefully assign different parts of the code to sub-channels. To reduce the number of design parameters and allow for efficient design, semi-regular allotted codes have been suggested. We first formulate the design of semi-regular codes as a mixed integer linear programming. Relaxing the semi-regularity constraint broadens the search space which results in improved codes and also a more efficient design via linear programming. While information theoretic results suggest that having channel state information-for a fixed power assignment-does not change the capacity, we show that under non-optimal decoding or when the maximum degree allowed in the code is small, allotted codes significantly outperform conventional ones. Finally, for the case that neither side has the channel knowledge (thus capacity-loss is inevitable), we see that the reduced capacity can still be approached by LDPC codes.

The optimal performance-complexity tradeoff for error-correcting codes at rates strictly below the Shannon limit is a central question in coding theory. This paper proposes a numerical approach for the minimization of decoding complexity for long-block-length irregular low-density parity-check (LDPC) codes. The proposed design methodology is applicable to any binary-input memoryless symmetric channel and any iterative message-passing decoding algorithm with a parallel-update schedule. A key feature of the proposed optimization method is a new complexity measure that incorporates both the number of operations required to carry out a single decoding iteration and the number of iterations required for convergence. This paper shows that the proposed complexity measure can be accurately estimated from a density-evolution and extrinsic-information transfer chart analysis of the code. A sufficient condition is presented for convexity of the complexity measure in the variable edge-degree distribution; when it is not satisfied, numerical experiments nevertheless suggest that the local minimum is unique. The results presented herein show that when the decoding complexity is constrained, the complexity-optimized codes significantly outperform threshold-optimized codes at long block lengths, within the ensemble of irregular codes.

In multiuser diversity systems, the impact of large-scale fading on the total system performance such as link quality and system power has not been widely addressed. Considering large-scale fading, we propose an adaptive multiuser scheduling to minimize the total system power while reducing the effect of large-scale fading on the system bit error rate. The number of active users is adapted to every shadow variation, which varies slower than small-scale fading. We consider the two widely used multiuser systems (i.e., delay-tolerant, and delay-sensitive multiuser systems). Closed-form expressions for the bit error rate are derived. The selection procedure for the minimum number of users is introduced for guaranteed performance of the above multiuser systems. The impact of adaptive multiuser diversity gain on the system power and bit error rate is illustrated over large-scale fading channels by numerical results.

Low-density parity-check (LDPC) codes have been used for communication over a two-user Gaussian broadcast channel. It has been shown in the literature that the optimal decoding of such system requires joint decoding of both user messages at each user. Also, a joint code design procedure should be performed. We propose a method which uses a novel labeling strategy and is based on the idea behind the bit-interleaved coded modulation. This method does not require joint decoding and/or joint code optimization. Thus, it reduces the overall complexity of near-capacity coding in broadcast channels. For different rate pairs on the boundary of the capacity region, pairs of LDPC codes are designed to demonstrate the success of this technique.

Design of low-density parity-check (LDPC) codes suitable for all channels which exhibit a given capacityCis investigated. Such codes are referred to as universal LDPC codes. First, based on numerous observations, a conjecture is put forth that a code working onNequal-capacity channels, also works on any convex combination of theseNchannels. As a supporting evidence, we prove that a code satisfying the stability condition onNchannels, also satisfies the stability condition on the convex hull of theseNchannels. Then, a channel decomposition method is suggested which spans any given channel with capacityCin terms of a number of identical-capacity basis channels. We expect codes that work on the basis channels to be suitable for any convex combination of the bases, i.e., all channels with capacityC. Such codes are found over a wide range of rates. An upper bound on the achievable rate of universal LDPC codes is suggested. Through examples, it is shown that our codes achieve rates extremely close to this upper bound. In comparison with existing LDPC codes designed for a given channel, significant performance gain is reported when codes are used over various channels of equal capacity.

An efficient method for analyzing the performance of finite-length low-density parity-check (LDPC) codes in the waterfall region, when transmission takes place on a memoryless binary-input output-symmetric channel is proposed. This method is based on studying the variations of the channel quality around its expected value when observed during the transmission of a finite-length codeword. We model these variations with a single parameter. This parameter is then viewed as a random variable and its probability distribution function is obtained. Assuming that a decoding failure is the result of an observed channel worse than the codeiquests decoding threshold, the block error probability of finite-length LDPC codes under different decoding algorithms is estimated. Using an extrinsic information transfer chart analysis, the bit error probability is obtained from the block error probability. Different parameters can be used for modeling the channel variations. In this work, two of such parameters are studied. Through examples, it is shown that this method can closely predict the performance of LDPC codes of a few thousand bits or longer in the waterfall region.

On a fading channel with no channel state information at the receiver, true log-likelihood ratios (LLR) are complicated functions of the channel output. It is assumed in the literature that the power of the additive noise is known and the expected value of the fading gain is used in a linear function of the channel output to find approximate LLRs. This approach, however, is not optimal in the sense of bit error rate performance. In this paper, we introduce a measure of accuracy for the approximate LLRs based on their probability density function and we show that this measure provides a very convenient tool for finding good approximate LLRs. Assuming that the power of the additive noise is known, and using the proposed measure, we find a linear LLR approximation whose performance is extremely close to that of the true LLR calculation on an uncorrelated Rayleigh fading channel. These results are then extended to the case that the noise power is also unknown and a performance almost identical to the previous case is obtained.

Low-density parity-check (LDPC) coding for a multitude of equal-capacity channels is studied. First, based on numerous observations, a conjecture is stated that when the belief propagation decoder converges on a set of equal-capacity channels, it would also converge on any convex combination of those channels. Then, it is proved that when the stability condition is satisfied for a number of channels, it is also satisfied for any channel in their convex hull. For the purpose of code design, a method is proposed which can decompose every symmetric channel with capacity C into a set of identical-capacity basis channels. We expect codes that work on the basis channels to be suitable for any channel with capacity C. Such codes are found and in comparison with existing LDPC codes that are designed for specific channels, our codes obtain considerable coding gains when used across a multitude of channels.

In event-driven wireless sensor networks, the network lifetime has a random nature due to the randomness of data reporting. The lifetime is even more nondeterministic when sensors are also deployed randomly. The lifetime of such a network is influenced by node deployment, initial energy of sensors, packet generation model and the number of sensors. This work quantifies the effect of these parameters on the lifetime of randomly deployed event-driven networks. First, the lifetime of individual sensors are studied. Then, an analytical expression is obtained for the complementary cumulative density function of the network lifetime. Such an analysis can be used for choosing the network parameter and efficiently optimizing the network lifetime. The results of this work are obtained for both multi- hop and single-hop wireless sensor networks and are verified with computer simulation. The approaches of this paper are shown to be applicable to more general cases.

Clustering sensors is considered as an efficient way for increasing the lifetime of a wireless sensor network. One of the main advantages of these networks, leading to a longer lifetime, is the ability of data aggregation by the cluster head (CH). Assuming a fixed-shape for the cluster, the probability of achieving a desired lifetime by the cluster has been derived when the nodes are randomly deployed within the cluster. Having the clusters lifetime, the network lifetime can be consequently determined. In addition, it is shown that clustered networks are not necessarily better than the non-clustered networks in terms of the energy consumption and consequently the network lifetime. To this end, a condition related to the data aggregation capability of CH is found indicating when the clustered networks outperform non-clustered ones.

An efficient method for finite-length low-density parity-check (LDPC) code analysis is proposed. This method is based on studying the channel variations when observed during a finite-length codeword. To this end, channel parameters are interpreted as random variables and their distributions are found. Assuming that a decoding failure is the result of an observed channel worse than the code's decoding threshold, the block error probability of finite-length LDPC codes is estimated. Using an extrinsic information transfer chart analysis, bit error probability is obtained from the block error probability. Our results suggest that by considering only the channel variations around its expected behavior and even ignoring the effects of cycles, one can closely predict the performance of LDPC codes of a few thousand bits or longer in the waterfall region.

The time-varying nature of wireless channels poses a challenge for using soft-decision iterative decoders on such channels. Even if the channel gain is perfectly known to the receiver, inaccurate estimation of the additive noise power, results in incorrect log-likelihood computation at the receiver and hence significant performance degradation in the decoder. Through a detailed study of the effects of channel estimation errors on the performance of soft-decision iterative decoders in uncorrelated block-fading channels, we propose a solution which does not need a knowledge of the power of the additive noise. We show that this solution performs almost identical to the case for which a perfect knowledge of the power of the additive noise exists at the receiver. The choice of the block-fading channel reflects a situation where the equivalent variance of the additive Gaussian noise can change in a wide range and thus the decoder performance seriously relies on the knowledge of the noise power at the receiver.

On a fading channel with no channel state information at the receiver, calculating true log-likelihood ratios (LLR) is complicated. Existing work assume that the power of the additive noise is known and use the expected value of the fading gain in a linear function of the channel output to find approximate LLRs. In this work, we first assume that the power of the additive noise is known and we find the optimum linear approximation of LLRs in the sense of maximum achievable transmission rate on the channel. The maximum achievable rate under this linear LLR calculation is almost equal to the maximum achievable rate under true LLR calculation. We also observe that this method appears to be the optimum in the sense of bit error rate performance too. These results are then extended to the case that the noise power is unknown at the receiver and a performance almost identical to the case that the noise power is perfectly known is obtained.

It is shown that regenerative relaying in a dual- hop diversity static or quasi-static relay channel can outperform non-regenerative relaying only if the source-relay link is reliable and power allocation to the source and the relay is optimized. In regenerative relaying, a maximal ratio combining receiver at the destination has an error floor at high signal-to-noise ratios. However, maximal ratio combining is not a maximum-likelihood structure in this application. Maximum-likelihood detection at the destination can remove this error floor, but cannot always make the performance of regenerative relaying surpass that of non- regenerative relaying. A hybrid protocol which avoids some of the limitations of previous relaying schemes is proposed. Conditions under which relaying increases the equivalent source-destination signal-to-noise ratio, and hence, the source-destination channel capacity are derived and the gain of the cooperation is calculated. The analysis provides quantitative measures for choosing the best relay among a set of candidates.

We propose a linear-programming approach to the design of low-density parity-check codes for non-uniform channels, i.e., when different bits of the codeword experience different channel parameters. Non-uniform channels are encountered in many communication systems, e.g., in a network that different packets are sent through parallel routes; in orthogonal frequency division multiplexing, where the codeword bits are modulated in different frequency bins with different SNR; also in multi-input multi-output systems, where different channel pairs have different parameters. We formulate the problem of optimizing the rate of an irregular low-density parity-check code, with guaranteed convergence over such a channel, as an iterative linear-programming. The number of design-parameters for code-design over non-uniform channels is much greater than the number of design-parameters in conventional channels. Therefore, search-based optimization methods are impractical. As a result, a linear-programming approach is significantly more efficient. The methodology of this paper is directly applicable to all decoding algorithms for which an exact or accurate-enough one-dimensional analysis is possible. For other decoding algorithms, we show that the method can still be applied after minor modifications.

Irregular decoding of low-density parity-check codes, i.e., using different algorithms in one iteration of the decoding of a single word, is studied. We formulate density evolution for irregular decoders. Using a one-dimensional representation of density evolution, we then jointly optimize irregular codes and irregular soft decoders for minimizing the decoding complexity. More specifically, for a given set of soft algorithms, a given channel, and a given code-rate, we find an irregular code-decoder pair which is capable of achieving a desired error performance with minimal decoding complexity. Robustness of irregular decoders when there exist channel estimation errors is also shown via an example

This paper considers a class of iterative message-passing decoders for low-density parity-check codes in which the decoder can choose its decoding rule from a set of decoding algorithms at each iteration. Each available decoding algorithm may have different per-iteration computation time and performance. With an appropriate choice of algorithm at each iteration, overall decoding latency can be reduced significantly, compared with standard decoding methods. Such a decoder is called a gear-shift decoder because it changes its decoding rule (shifts gears) in order to guarantee both convergence and maximum decoding speed (minimum decoding latency). Using extrinsic information transfer charts, the problem of finding the optimum (minimum decoding latency) gear-shift decoder is formulated as a computationally tractable dynamic program. The optimum gear-shift decoder is proved to have a decoding threshold equal to or better than the best decoding threshold among those of the available algorithms. In addition to speeding up software decoder implementations, gear-shift decoding can be applied to optimize a pipelined hardware decoder, minimizing hardware cost for a given decoder throughput.

This paper considers a class of iterative message-passing decoders for low-density parity-check codes in which the decoder can choose its decoding rule from a set of decoding algorithms at each iteration. Each available decoding algorithm may have a different per-iteration computation time and performance. With an appropriate choice of algorithm at each iteration, overall decoding latency can be reduced significantly, compared with standard decoding methods. Such a decoder is called a gear-shift decoder because it changes its decoding rule (shifts gears) in order to guarantee both convergence and maximum decoding speed (minimum decoding latency). Using extrinsic information transfer charts, the problem of finding the optimum (minimum decoding latency) gear-shift decoder is formulated as a computationally tractable dynamic program. The optimum gear-shift decoder is proved to have a decoding threshold equal to or better than the best decoding threshold among those of the available algorithms. In addition to speeding up software decoder implementations, gear-shift decoding can be applied to optimize a pipelined hardware decoder, minimizing hardware cost for a given decoder throughput

A new modulation method for linear space-time codes is proposed based on using constellations of different sizes for different symbols. It is shown that the proposed method significantly reduces the complexity of the sphere decoding algorithm. The complexity reduction is more pronounced in high-rate codes, where each code matrix carries a large number of symbols. We also show that the choice of constellation size provides a tradeoff between performance and complexity. Using this, some guidelines for choosing constellation size are presented. As one introduces more constellation disparity in the code, the complexity is further reduced, while the performance loss grows. Typically, a complexity reduction of one to two orders of magnitude can be achieved at the expense of about 3 dB coding gain. We suggest a simple modification in our design to reduce this loss to about 2 dB.

We consider an iterative message-passing decoder that can choose its decoding rule among a group of decoding algorithms at each iteration (for example: a software decoder). Each available decoding algorithm may have a different computation time and performance. We first show that with proper choice of algorithm at each iteration, decoding latency can significantly be reduced. We call such a decoder a gear-shift decoder because it changes its decoding rule (shifts gear) in order to guarantee both convergence and minimum decoding-latency. We also prove that the optimum gear-shift decoder (the one with the minimum decoding-latency) has a decoding threshold equal to or better than the best decoding threshold of the available algorithms. We use extrinsic information transfer charts and dynamic programming to find the optimum gear-shift decoder.

A new modulation method for linear space-time codes is proposed based on using constellations of different sizes for different symbols. It is shown that the proposed method significantly reduces the complexity of the sphere decoding algorithm. Typically, a complexity reduction of one to two orders of magnitude can be achieved at the expense of about 3 dB coding gain. With a simple modification in our design, we reduce this loss to about 2 dB.

The complexity-rate tradeoff for error-correcting codes below the Shannon limit is a central question in coding theory. This paper makes progress in this area by presenting a joint numerical optimization of rate and decoding complexity for low-density parity-check codes. The focus of this paper is on the binary symmetric channel and on a class of decoding algorithms for which an exact extrinsic information transfer (EXIT) chart analysis is possible. This class of decoding algorithms includes the Gallager decoding algorithm B. The main feature of the optimization method is a complexity measure based on the EXIT chart that accurately estimates the number of iterations required for the decoding algorithm to reach a target error rate. Under a fixed check-degree distribution, it is shown that the proposed complexity measure is a convex function of the variable-degree distribution in a region of interest. This allows us to numerically characterize the complexity-rate tradeoff. We show that for the Gallager B decoding algorithm on binary symmetric channels, the optimization procedure can produce complexity savings of 30-40% as compared to the conventional code design method

We consider a class of message-passing decoders for low-density parity-check (LDPC) codes whose messages are binary valued. We prove that if the channel is symmetric and all codewords are equally likely to be transmitted, an optimum decoding rule (in the sense of minimizing message error rate) should satisfy certain symmetry and isotropy conditions. Using this result, we prove that Gallager's Algorithm B achieves the optimum decoding threshold among all binary message-passing decoding algorithms for regular codes. For irregular codes, we argue that when the nodes of the message-passing decoder do not exploit knowledge of their decoding neighborhood, optimality of Gallager's Algorithm B is preserved. We also consider the problem of designing irregular LDPC codes and find a bound on the achievable rates with Gallager's Algorithm B. Using this bound, we study the case of low error-rate channels and analytically find good degree distributions for them.

We apply irregular low-density parity-check (LDPC) codes to the design of multilevel coded quadrature amplitude modulation (QAM) schemes for application in discrete multitone systems in frequency-selective channels. A combined Gray/Ungerboeck scheme is used to label each QAM constellation. The Gray-labeled bits are protected using an irregular LDPC code with iterative soft-decision decoding, while other bits are protected using a high-rate Reed-Solomon code with hard-decision decoding (or are left uncoded). The rate of the LDPC code is selected by analyzing the capacity of the channel seen by the Gray-labeled bits and is made adaptive by selective concatenation with an inner repetition code. Using a practical bit-loading algorithm, we apply this coding scheme to an ensemble of frequency-selective channels with Gaussian noise. Over a large number of channel realizations, this coding scheme provides an average effective coding gain of more than 7.5 dB at a bit-error rate of 10/sup -7/ and a block length of approximately 10/sup 5/ b. This represents a gap of approximately 2.3 dB from the Shannon limit of the additive white Gaussian noise channel, which could be closed to within 0.8-1.2 dB using constellation shaping.

We introduce a new one-dimensional (1-D) analysis of low-density parity-check (LDPC) codes on additive white Gaussian noise channels which is significantly more accurate than similar 1-D methods. Our method assumes a Gaussian distribution in message-passing decoding only for messages from variable nodes to check nodes. Compared to existing work, which makes a Gaussian assumption both for messages from check nodes and from variable nodes, our method offers a significantly more accurate estimate of convergence behavior and threshold of convergence. Similar to previous work, the problem of designing irregular LDPC codes reduces to a linear programming problem. However, our method allows irregular code design in a wider range of rates without any limit on the maximum variable-node degree. We use our method to design irregular LDPC codes with rates greater than 1/4 that perform within a few hundredths of a decibel from the Shannon limit. The designed codes perform almost as well as codes designed by density evolution.