Stacked intelligent metasurfaces (SIMs) have recently emerged as an effective solution for next-generation wireless networks. A SIM comprises multiple metasurface layers that enable signal processing directly in the wave domain. Moreover, recent advances in flexible metamaterials have highlighted the potential of flexible intelligent metasurfaces (FIMs), which can be physically morphed to enhance communication performance. In this paper, we propose a stacked flexible intelligent metasurface (SFIM)-based communication system for the first time, where each metasurface layer is deformable to improve the system's performance. We first present the system model, including the transmit and receive signal models as well as the channel model, and then formulate an optimization problem to maximize the system sum rate under constraints on the transmit power budget, morphing distance, and the unit-modulus condition of the meta-atom responses. To solve this problem, we develop an alternating optimization framework based on the gradient projection method. Simulation results demonstrate that the proposed SFIM-based system achieves significant performance gains compared to its rigid SIM counterpart.

Integrated sensing and communication (ISAC) has been recognized as one of the key technologies capable of simultaneously improving communication and sensing services in future wireless networks. Moreover, the introduction of recently developed movable antennas (MAs) has the potential to further increase the performance gains of ISAC systems. Achieving these gains can pose a significant challenge for MA-enabled ISAC systems operating in the near-field due to the corresponding spherical wave propagation. Motivated by this, in this paper we maximize the weighted sum rate (WSR) for communication users while maintaining a minimal sensing requirement in an MA-enabled near-field ISAC system. To achieve this goal, we propose an algorithm that optimizes the sensing receive combiner, the communication precoding matrices, the sensing transmit beamformer and the positions of the users' MAs in an alternating manner. Simulation results show that using MAs in near-field ISAC systems provides a substantial performance advantage compared to near-field ISAC systems with only fixed antennas. Additionally, we demonstrate that the highest WSR is obtained when larger weights are allocated to the users placed closer to the BS, and that the sensing performance is significantly more affected by the minimum sensing signal-to-interference-plus-noise ratio (SINR) threshold compared to the communication performance.

Carrier mode shift keying (CMSK) is a recently proposed waveform-domain index modulation scheme that improves the spectral efficiency (SE) of hybrid carrier (HC) communication systems. This innovative scheme simultaneously transmits information bits mapped to the traditional constellation symbols as well as information bits mapped to the index of the weighted-type fractional Fourier transform (WFRFT) parameter. In this paper, we propose an enhanced version of CMSK (E-CMSK) that introduces a subblock precoding module at the transmitter side. Compared with CMSK, E-CMSK conveys index information through subblock-level parameter mapping, thereby further improving the SE. Furthermore, E-CMSK provides enhanced system flexibility, enabling trade-offs among the SE, reliability and detection complexity through subblock size adjustment. To address the prohibitive complexity of the maximum likelihood (ML) detector, a low-complexity sequential detector based on linear frequency domain equalization (FDE) is developed, which reduces the computational complexity from exponential to linear. Furthermore, to compensate for the performance loss inherent in linear equalization, an enhanced iterative block decision feedback equalization (IB-DFE) detector is proposed. This iterative scheme effectively suppresses residual interference, enabling the system to approach the global ML performance. An analytical expression for the average overall bit error rate (BER) is derived to provide theoretical performance insights. While this expression reveals the impact of key parameters like Euclidean distance, its complexity makes it intractable for direct optimization. Therefore, we directly analyze the Euclidean distance distribution of the E-CMSK constellation as an intuitive yet effective tool for system design. This analysis guides the design of a Gray-coded bit-parameter mapping scheme and an equally spaced WFRFT parameter selection strategy, which aims to improve the overall BER performance. Simulation results demonstrate that the proposed E-CMSK scheme outperforms the conventional HC system in multi-path fading channels, particularly at high SNRs.

Integrated sensing and communication (ISAC) has emerged as a promising technology for sixth-generation (6G) communication networks. At the same time, ensuring the privacy of targets in ISAC is important in contexts where a malicious sensor is present. In this paper, we investigate a reconfigurable intelligent surface (RIS)-assisted ISAC system designed to protect a sensing region against an adversarial detector (AD), where the base station (BS) has imperfect knowledge of the AD’s location. The RIS consists of both reflecting and absorptive elements (the latter serving as sensing elements), which can be adaptively reconfigured to meet system requirements. Specifically, the system is designed to maximize the jamming power from the BS to the AD by jointly optimizing the transmit beamformer at the BS, the RIS phase-shift matrix, the receive beamformer at the RIS, and the allocation between reflecting and absorptive elements at the RIS while ensuring a minimum sensing signal-to-interference-plus-noise ratio (SINR) at sample points within the sensing region, as well as a minimum communication SINR for each user. To address this challenging optimization problem, we propose an alternating optimization framework combined with a successive convex approximation method tailored for each subproblem. Our results show that the proposed system model offers significant protection of the sensing area compared to the case where the target privacy is not considered. Simulations also confirm that the proposed adaptive RIS partitioning outperforms the fixed RIS partitioning approach.

Active reconfigurable intelligent surfaces (RISs) can improve the performance of integrated sensing and communication (ISAC), and therefore enable simultaneous data transmission and target sensing. However, when the line-of-sight (LoS) link between the base station and the sensing target is blocked, the sensing signals suffer from severe path loss, resulting in an inferior sensing performance. To address this issue, this paper employs a sensor-aided active RIS to enhance ISAC system performance. The goal is to maximize the signal-to-noise ratio of the echo signal from the target at the sensor-array while meeting constraints on communication signal quality, power budgets, and RIS amplification limits. The optimization problem is challenging due to its non-convex nature and the coupling between the optimization variables. We propose a closed-form solution for receive beamforming, and a successive convex approximation based iterative method for transmit and reflection beamforming design. Simulation results demonstrate the advantage of the proposed sensor-aided active RIS-assisted system model over its non-sensor-aided counterpart.

In this paper, we propose a semi-analytical method to design polar codes for the reconfigurable intelligent surface (RIS)-assisted channel with Rayleigh fading on each wireless link, while also providing an approximate closed-form expression for its word error probability (WEP) as a function of the number of RIS elements. Conventional polar code design methods involve numerically evaluated values of the bit-channel transition probabilities used to obtain the WEP upper bound in which the impact of the number of RIS elements, signal-to-noise ratio (SNR), and code rate is challenging to analyze. In contrast, our approach uses exponential approximations to obtain approximate closed-form expressions for the bit-channel transition probabilities. These exponential terms can be succinctly characterized in terms of coefficient pairs (CPs) which can be tracked numerically during code design and are approximately independent of the SNR and the number of RIS elements. This allows for rapid design of polar codes for any combination of the RIS elements and SNR. Numerical and simulation results show that the proposed method efficiently predicts the required number of RIS elements for a target WEP within the range of$10^{\text {-}2}$and$10^{\text {-}6}$, and can also be used to optimize resource allocation in a multiuser context.

Users in millimeter-wave (mmWave) systems often exhibit diverse channel strengths, which can negatively impact user fairness in resource allocation. Moreover, exact channel state information (CSI) may not be available at the transmitter, rendering suboptimal resource allocation. In this paper, we address these issues within the context of energy efficiency maximization in reconfigurable intelligent surface (RIS)-assisted mmWave systems. We first derive a tractable lower bound on the achievable sum rate, taking into account CSI errors. Subsequently, we formulate the optimization problem, targeting maximizing the system energy efficiency while maintaining a minimum Jain’s fairness index controlled by a tunable design parameter. The optimization problem is very challenging due to the coupling of the optimization variables in the objective function and the fairness constraint, as well as the existence of non-convex equality and fractional constraints. To solve this optimization problem, we employ the penalty dual decomposition method, together with a projected gradient ascent based alternating optimization procedure. The proposed algorithm exhibits linear time complexity with respect to the number of RIS elements. Simulation results demonstrate that the proposed algorithm can achieve an optimal energy efficiency for a prescribed Jain’s fairness index. In addition, adjusting the fairness design parameter can yield a favorable trade-off between energy efficiency and user fairness compared to methods that exclusively focus on optimizing one of these metrics.

Topological quantum codes, such as toric and surface codes, are excellent candidates for hardware implementation due to their robustness against errors and their local interactions between qubits. However, decoding these codes efficiently remains a challenge: existing decoders often fall short of meeting requirements such as having low computational complexity (ideally linear in the code’s blocklength), low decoding latency, and low power consumption. In this paper we propose a novel bit-flipping (BF) decoder tailored for toric and surface codes. We introduce the proximity vector as a heuristic metric for flipping bits, and we develop a new subroutine for correcting degenerate multiple errors on adjacent qubits. Our algorithm has quadratic complexity growth and it can be efficiently implemented as it does not require operations on dynamic memories, as do state-of-art decoding algorithms such as minimum weight perfect matching or union find. The proposed decoder shows a decoding threshold of 7.5% for the 2D toric code and 7% for the rotated planar code over the binary symmetric channel.

We propose a novel bit-flipping (BF) decoder tailored for toric codes. We introduce the proximity vector as a heuristic metric for flipping bits, and we develop a new subroutine for correcting a particular class of harmful degenerate errors. Comparing to other decoders, our algorithm is particularly suitable for efficient hardware implementation as it does not require operations on dynamic memories. The proposed decoder shows a decoding threshold of 7.5% for the 2D toric code over the binary symmetric channel.

This paper proposes two approaches for reducing the impact of the error floor phenomenon when decoding quantum low-density parity-check codes with belief propagation based algorithms. First, a low-complexity syndrome-based linear programming (SB- LP) decoding algorithm is proposed, and second, the proposed SB-LP is applied as a post-processing step after syndrome-based min-sum (SB-MS) decoding. For the latter case, a new early stopping criterion is introduced to decide when to activate the SB- LP algorithm, avoiding executing a predefined maximum number of iterations for the SB-MS decoder. Simulation results show, for a sample hypergraph code, that the proposed decoder can lower the error floor by two to three orders of magnitude compared to SB-MS for the same total number of decoding iterations.

In this paper, we propose an opportunistic user scheduling scheme in a multi-user reconfigurable intelligent surface (RIS) aided wireless system to improve secrecy. We derive the secrecy outage probability (SOP) and its asymptotic expression in approximate closed form. The asymptotic analysis shows that the SOP does not depend on the transmitter-to-RIS distance and saturates at a high signal-to-noise ratio to a fixed value that depends on the ratio of the path-loss of the RIS-to-destination and RIS-to-eavesdropper links and the number of users. It is shown that the asymptotic SOP decreases exponentially with the number of RIS elements. We also compare the secrecy performance of our scheme with that of a non-orthogonal multiple access (NOMA) scheduling scheme, which chooses a pair of users to schedule in each time slot. The comparison shows that the secrecy performance of the NOMA scheme is compromised and that our proposed scheduling scheme has better performance.

In this paper, reconfigurable intelligent surface (RIS)-assisted generalized receive quadrature spatial modulation (RIS-GRQSM) is proposed to improve the spectral efficiency of RIS-aided quadrature spatial modulation (QSM) systems by utilizing the concept of generalized spatial modulation (GSM). That is, multiple antennas are activated at the receiver independently for both the real and imaginary parts. We propose a max-min optimization problem to adjust the phase shifts of all RIS elements to maximize the relevant signal-to-noise ratios (SNRs) at all activated receive antennas. Using Lagrange duality, the non-convex optimization problem involving the phase shifts of all RIS elements reduces to a convex optimization involving a number of variables equal to the number of activated receive antennas. A successive greedy detector (GD) can be used at the receiver to detect the active antennas, which simplifies the detection process. The numerical results show that the proposed scheme outperforms the benchmark schemes in terms of error rate performance, especially in systems with a larger number of receive antennas. In the special case where each receive antenna corresponds to a user and is activated, the RIS-GRQSM system becomes a multicast communication system. In this context, in contrast to existing phase shift optimization algorithms which exhibit an impractical level of complexity, our proposed solution offers the advantage of low complexity and practical feasibility of implementation.

Integrated sensing and communication (ISAC) is expected to be offered as a fundamental service in the upcoming sixth-generation (6G) communications standard. However, due to the exposure of information-bearing signals to the sensing targets, ISAC poses unique security challenges. In recent years, intelligent reflecting surfaces (IRSs) have emerged as a novel hardware technology capable of enhancing the physical layer security of wireless communication systems. Therefore, in this paper, we consider the problem of transmit and reflective beamforming design in a secure IRS-enabled ISAC system to maximize the beampattern gain at the target. The formulated non-convex optimization problem is challenging to solve due to the intricate coupling between the design variables. Moreover, alternating optimization (AO) based methods are inefficient in finding a solution in such scenarios, and convergence to a stationary point is not theoretically guaranteed. Therefore, we propose a novel successive convex approximation (SCA)-based second-order cone programming (SOCP) scheme in which all of the design variables are updated simultaneously in each iteration. The proposed SCA-based method significantly outperforms a penalty-based benchmark scheme previously proposed in this context. Moreover, we also present a detailed complexity analysis of the proposed scheme, and show that despite having slightly higher per-iteration complexity than the benchmark approach the average problem-solving time of the proposed method is notably lower than that of the benchmark scheme.

Reconfigurable intelligent surfaces (RISs) are considered to be a promising solution to overcome the blockage issue in the millimeter-wave (mmWave) band. Energy efficiency is an important performance metric in RIS-assisted mmWave systems with a large number of antennas. However, due to the severe path loss in mmWave systems, resource allocation algorithms tend to allocate most of the resources for the benefit of the users with higher channel gains. In this paper, we propose a lexicographic-based approach to find the optimal power allocation, RIS passive beamforming matrix, and analog precoders that maximize both energy efficiency and user fairness. We solve the corresponding multi-objective optimization problem in two stages. In the first stage, we maximize the energy efficiency, and in the second stage we maximize the fairness subject to a minimum energy efficiency constraint. We propose an alternating optimization procedure to solve the optimization problem in each stage. The optimal power allocation is found using Dinkelbach's method and convex optimization techniques in the first and second stage respectively, the RIS phase shift matrix is found using a gradient ascent algorithm, and the analog precoder is determined using beam alignment. Numerical results show that the proposed algorithm can achieve an excellent trade-off between the energy efficiency and fairness by boosting the minimum weighted rate with a minor and controllable reduction in the energy efficiency.

This paper focuses on the fundamental problem of maximizing the achievable weighted sum rate (WSR) at information receivers (IRs) in an intelligent reflecting surface (IRS) assisted simultaneous wireless information and power transfer system under a multiple-input multiple-output (SWIPT-MIMO) setting, subject to a quality-of-service (QoS) constraint at the energy receivers (ERs). Notably, due to the coupling between the transmit precoding matrix and the passive beamforming vector in the QoS constraint, the formulated non-convex optimization problem is challenging to solve. We first decouple the design variables in the constraints following a penalty dual decomposition method, and then apply an alternating gradient projection algorithm to achieve a stationary solution to the reformulated optimization problem. The proposed algorithm nearly doubles the WSR compared to that achieved by a block-coordinate descent (BCD) based benchmark scheme. At the same time, the complexity of the proposed scheme grows linearly with the number of IRS elements while that of the benchmark scheme is proportional to the cube of the number of IRS elements.

This paper investigates the performance of a time-switching (TS) based cooperative non-orthogonal multiple access (NOMA) network consisting of a base station (BS), a near user (NU), a distant user (DU), and a full-duplex (FD) relay. The BS shares a direct link to the NU, while communication to the DU is assisted by a battery-aided energy harvesting FD relay. We consider a static battery energy (SBE) scheme in which a fixed amount of battery energy augments the harvested energy and analyze the performance of both NU and DU. Also, a new dynamic battery energy (DBE) scheme, wherein the harvested energy is augmented with as little battery energy as possible in order to achieve desired quality of service, is proposed and is shown to ensure efficient battery utilization. Considering a threshold-based nonlinear EH model, closed-form expressions are derived for the throughput of NU and DU for both SBE and DBE schemes. Furthermore, for the DBE scheme, we also derive an exact closed-form expression for the average battery energy drawn per symbol interval. We then demonstrate that the choice of battery energy and TS parameter is crucial to attain a maximum DU throughput while simultaneously guaranteeing a target throughput at the NU.

In this paper, we propose a novel reconfigurable intelligent surface (RIS)-assisted wireless communication scheme which uses the concept of spatial modulation, namely RIS-assisted receive quadrature spatial modulation (RIS-RQSM). In the proposed RIS-RQSM system, the information bits are conveyed via both the indices of the two selected receive antennasandthe conventional in-phase/quadrature (IQ) modulation. We propose a novel methodology to adjust the phase shifts of the RIS elements in order to maximize the signal-to-noise ratio (SNR)andat the same time toconstructtwo separate PAM symbols at the selected receive antennas, as the in-phase and quadrature components of the desired IQ symbol. An energy-based greedy detector (GD) is implemented at the receiver to efficiently detect the received signal with minimal channel state information (CSI) via the use of an appropriately designed one-tap pre-equalizer. We also derive a closed-form upper bound on the average bit error probability (ABEP) of the proposed RIS-RQSM system. Then, we formulate an optimization problem to minimize the ABEP in order to improve the performance of the system, which allows the GD to act as a near-optimal receiver. Extensive numerical results are provided to demonstrate the error rate performance of the system and to compare with that of a prominent benchmark scheme. The results verify the remarkable superiority of the proposed RIS-RQSM system over the benchmark scheme.

Orthogonal time frequency space (OTFS) modulation has recently emerged as a potential 6G candidate waveform which provides improved performance in high-mobility scenarios. In this paper we investigate the combination of OTFS with non-orthogonal multiple access (NOMA). Existing equalization and detection methods for OTFS-NOMA, such as minimum-mean-squared error with successive interference cancellation (MMSE-SIC), suffer from poor performance. Additionally, existing iterative methods for single-user OTFS based on low-complexity iterative least-squares solvers are not directly applicable to the NOMA scenario due to the presence of multi-user interference (MUI). Motivated by this, in this paper we propose a low-complexity method for equalization and detection for OTFS-NOMA. The proposed method uses a novel reliability zone (RZ) detection scheme which estimates the reliable symbols of the users and then uses interference cancellation to remove MUI. The thresholds for the RZ detector are optimized in a greedy manner to further improve detection performance. In order to optimize these thresholds, we modify the least squares with QR-factorization (LSQR) algorithm used for channel equalization to compute the post-equalization mean-squared error (MSE), and track the evolution of this MSE throughout the iterative detection process. Numerical results demonstrate the superiority of the proposed equalization and detection technique to the existing MMSE-SIC benchmark in terms of symbol error rate (SER).

With the advancement of wireless communication technologies, reconfigurable intelligent surfaces (RISs) have recently paved the way to augmenting the performance of wireless networks with the aid of multiple reflecting surfaces by efficiently attuning the signal reflection through a large number of low-cost passive elements. In this paper, we consider an RIS-aided full-duplex (FD) communication network consisting of a FD access point (AP) that communicates with an uplink and a downlink user simultaneously with the aid of an RIS as well as through the direct link between the AP and users. To evaluate the system performance under infinite blocklength (IBL) and finite blocklength (FBL) codes, we derive the analytical expressions for the outage probability and throughput in case of IBL, and for block-error rate (BLER) and goodput in the case of FBL, for both uplink and downlink transmission. Furthermore, the expressions for the maximum achievable rate under FBL and IBL transmission are derived. Next, we also extend the analysis of the single-user framework to a more practical scenario with multiple users utilizing non-orthogonal multiple access (NOMA) and derive analytical expressions for the outage probability and BLER at each downlink user and at the AP. The accuracy of the derived expressions is validated via simulation results, and insights are provided regarding the impact of the number of reflecting elements and imperfect channel state information (CSI) on the performance of the considered system. Finally, from the comparative analysis, it is shown that the RIS-aided system outperforms the system without RIS in both IBL and FBL scenarios, providing remarkable improvement in the outage probability and BLER.

The recent advent of simultaneous refracting and re-flecting reconfigurable intelligent surface (STAR-RIS) has paved the way for next generation wireless technology by enhancing the quality of the signal with wider coverage area connectivity. In this work, we propose a novel STAR-RIS assisted full duplex (FD) wireless communication system where a FD base station (BS) communicates with an uplink user and a downlink user simultaneously with the aid of a STAR-RIS. First, we derive the probability density function (PDF) of the uplink and downlink signal to interference plus noise ratio (SINR). Using the derived PDF, we analyze the system performance and derive analytical closed-form expressions for the outage probability and achievable throughput for both the uplink and downlink communication. Finally, we validate the accuracy of the derived analytical expressions using Monte-Carlo simulations and show that the use of the STAR- RIS provides a significantly improved performance compared to the conventional RIS.

This paper analyzes the secrecy performance of a reconfigurable intelligent surface (RIS) assisted wireless communication system with a friendly jammer in the presence of an eavesdropper. The friendly jammer enhances the secrecy by introducing artificial noise towards the eavesdropper without degrading the reception at the destination. Approximate secrecy outage probability (SOP) is derived in closed form. We also provide a simpler approximate closed-form expression for the SOP in order to understand the effect of system parameters on the performance and to find the optimal power allocation for the transmitter and jammer. The optimal transmit and jamming power allocation factor is derived by minimizing the SOP assuming a total power constraint. It is shown that the SOP performance is significantly improved by the introduction of the jammer and a gain of approximately 3 dB is achieved at an SOP of 10–4by optimally allocating power compared to the case of equal power allocation.

Abstract Ultra‐reliable low‐latency communication (URLLC) has gained significant interest since it deals with short packet transmission adopted to reduce latency; however, this implies that the conventional Shannon capacity formula is not applicable, and the achievable data rate becomes a complex function of the decoding error probability and blocklength. This paper studies URLLC transmission using a time‐division multiple access scheme with an arbitrary number of actuators utilising a reconfigurable intelligent surface. The authors optimisze the weighted sum rate of this system subject to reliability, total energy, and latency constraints. For the blocklength allocation in a scenario where each actuator is allocated equal power, a closed‐form analytical solution is provided. Also, for the case of joint optimization of the blocklength and power of each actuator, an analytical solution is provided for the case of two actuators, while an iterative sequential quadratic programing method is adopted for the case of an arbitrary number of actuators. The proposed methodology provides a low‐complexity, fast solution, which is more efficient than using exhaustive search techniques. The results show that in some cases, optimization of the blocklength provides a near‐optimal solution at low complexity, while jointly optimising the blocklength and the power per actuator has an improved performance at the cost of additional complexity.

In this paper, we propose a novel transmission scheme, calledsparse layered MIMO(SL-MIMO), that combines non-orthogonal transmission and singular value decomposition (SVD) precoding. Non-orthogonality in SL-MIMO allows re-using of the eigen-channels which improves the spectral efficiency and error rate performance of the system through enhancing the coding gain and diversity gain. We also present a low-complexity message-passing (MP) detector for the proposed SL-MIMO system which performs quite close to maximum likelihood (ML). The joint moment generating function (MGF) of theorderedeigenvalues is calculated and used to derive a closed-form upper bound on the average word error probability (AWEP) of the SL-MIMO system, and this derived expression is then used to analyze the diversity gain of the system. We use our analytical results to design sub-optimal codebooks to minimize the error rate of the SL-MIMO system. Simulation results in$4\times 4$and$6\times 6$multiple-input multiple-output (MIMO) systems with 4-ary, 16-ary, and 64-ary constellations show that our proposed SL-MIMO scheme outperforms competing approaches such as X- and Y-codes in terms of system error rate performance. SL-MIMO has 5.6 dB advantage compared to X-codes and 4.7 dB advantage compared to Y-codes in$6\times 6$MIMO system with a 64-ary constellation.

Reconfigurable intelligent surfaces (RISs) represent a promising candidate for sixth-generation (6G) wireless networks, as the RIS technology provides a new solution to control the propagation channel in order to improve the efficiency of a wireless link through enhancing the received signal power. In this paper, we propose RIS-assisted receive quadrature space shift keying (RIS-RQSSK), which enhances the spectral efficiency of an RIS-based index modulation (IM) system by using the real and imaginary dimensions independently for the purpose of IM. Therefore, the error rate performance of the system is improved as all RIS elements reflect the incident transmit signal toward both selected receive antennas. At the receiver, a low-complexity but effective greedy detector (GD) can be employed which determines the maximum energy per dimension at the receive antennas. A max-min optimization problem is defined to maximize the received signal-to-noise ratio (SNR) components at both selected receive antennas; an analytical solution is provided based on Lagrange duality. In particular, the multi-variable optimization problem is shown to reduce to the solution of a single-variable equation, which results in a very simple design procedure. In addition, we investigate the average bit error probability (ABEP) of the proposed RIS-RQSSK system and derive a closed-form approximate upper bound on the ABEP. We also provide extensive numerical simulations to validate our derivations. Numerical results show that the proposed RIS-RQSSK scheme substantially outperforms recent prominent benchmark schemes. This enhancement considerably increases with an increasing number of receive antennas.

Ultra-reliable low-latency communication (URLLC) is one of the most important components in the fifth generation (5G) cellular networks for realizing mission-critical applications. In this paper, we jointly optimize the transceiver design and decoding error probability (DEP) of a full-duplex (FD) URLLC system, where the base station (BS) operates in FD mode, while the uplink (UL) and downlink (DL) users work in half-duplex (HD) mode. Accordingly, an optimization problem is formulated to maximize the achievable total (UL plus DL) rate for an FD URLLC system under finite blocklength, subject to the end-to-end (E2E) reliability constraint from the UL user to each DL user and the total transmission power constraint at the UL user and at the BS. We analyze the problem structure and convexify the problem by approximating the channel dispersion in scenarios of high and mid-to-high signal-to-interference plus noise ratio (SINR) regimes, respectively. Next, efficient iterative algorithms are proposed to find the near-optimal power allocation for the UL user and transceiver weights for the BS. Furthermore, closed-form expressions of the transceiver weights are derived, and the convergence of the proposed algorithms is proved. Simulation examples demonstrate the impact of the code blocklength, number of DL users, transmitter/receiver distortion and DEP threshold on the system performance.

Reconfigurable intelligent surface (RIS) assisted radio is considered as an enabling technology with great potential for the sixth-generation (6G) wireless communications standard. The achievable secrecy rate (ASR) is one of the most fundamental metrics to evaluate the capability of facilitating secure communication for RIS-assisted systems. However, the definition of ASR is based on Shannon's information theory, which generally requires long codewords and thus fails to quantify the secrecy of emerging delay-critical services. Motivated by this, in this paper we investigate the problem of maximizing the secrecy rate under a delay-limited quality-of-service (QoS) constraint, termed as the effective secrecy rate (ESR), for an RIS-assisted multiple-input single-output (MISO) wiretap channel subject to a transmit power constraint. We propose an iterative method to find a stationary solution to the formulated non-convex optimization problem using a block coordinate ascent method (BCAM), where both the beamforming vector at the transmitter as well as the phase shifts at the RIS are obtained in closed forms in each iteration. We also present a convergence proof, an efficient implementation, and the associated complexity analysis for the proposed method. Our numerical results demonstrate that the proposed optimization algorithm converges significantly faster that an existing solution. The simulation results also confirm that the secrecy rate performance of the system with stringent delay requirements reduces significantly compared to the system without any delay constraints, and that this reduction can be significantly mitigated by an appropriately placed large-size RIS.

Multilevel coding (MLC) is a coded modulation technique which can achieve excellent performance over a range of communication channels. Polar codes have been shown to be quite compatible with communication systems using MLC, as the rate allocation of the component polar codes follows the natural polarization inherent in polar codes. MLC based techniques have not yet been studied in systems that use spatial modulation (SM). SM makes the polar code design difficult as the spatial bits actually select a channel index for transmission. To solve this problem, we propose a Monte Carlo based evaluation of the ergodic capacities for the individual bit levels under the capacity rule for a space-shift keying (SSK) system, where we also make use of a single antenna activation to approximate the transmission channel for the design of the multilevel polar code. Our simulation results show that the multilevel polar coded 16 × 1 SSK system outperforms the corresponding system that uses bit-interleaved polar coded modulation by 2.9 dB at a bit error rate (BER) of 10−4.

In this paper, a communication network using single carrier with cyclic prefix modulation over frequency selective channels is considered, where an access point provides connectivity to a legitimate destination through multiple transmitters with unreliable backhaul links in the presence of an eavesdropper. A sub-optimal and an optimal transmitter selection scheme are proposed to improve the secrecy of the system, depending on whether the active backhaul channel knowledge is available a priori or not. The secrecy outage probability (SOP) and its asymptotic limit are presented in closed-form. This provides some insights regarding how knowledge of the active backhaul links affects the secrecy performance of the network. Our results show that the optimal transmitter selection scheme obtains a larger benefit than the sub-optimal scheme from the knowledge of the active backhaul links, resulting in a significantly improved system performance; however, the sub-optimal transmitter selection scheme can reduce the complexity and feedback overhead.

In this paper we consider the problem of computing the capacity of multi-user Gaussian MIMO systems under multiple linear transmit covariance constraints (LTCCs). These LTCCs are general enough to include many transmit power constraints such as sum power constraint (SPC) or per-antenna power constraint (PAPC) as special cases. For the considered MIMO systems with multiple LTCCs, existing solutions are based on subgradient or gradient descent methods, which are known to have slow convergence in general and are therefore not applicable to massive MIMO systems. In contrast, we propose a low-complexity semi-closed-form approach to computing the MIMO capacity for the system of interest. To this end, the considered problem in the broadcast channel is transformed into an equivalent minimax problem in the multiple access channel. The special structure of the minimax problem allows us to derive water-filling-like algorithms based on a novel combination of alternating optimization and concave-convex procedure. For the important case of joint SPC and PAPC, we also propose analytical expressions to find the optimal covariance matrix. Extensive analytical and numerical results are provided to demonstrate the effectiveness of our approach under various massive MIMO system settings.

A small-cell network with multiple transmitters and unreliable wireless backhaul is considered for secrecy enhancement. The small-cell network is operating under a spectrum sharing agreement with a primary network in a cognitive radio system. A constraint on the desired outage probability at the primary receiver is assumed as a part of the spectrum sharing agreement. The reliability of the wireless backhaul links are modeled by a set of independent and identically distributed Bernoulli random variables. A sub-optimal and an optimal small-cell transmitter selection (TS) scheme is proposed to improve the performance of the system, depending on the availability of channel state information. Selection schemes are designed for the scenario where knowledge is available regarding which backhaul links are active. The corresponding secrecy outage probabilities along with their asymptotic expressions are derived. It is shown that the secrecy performance is significantly improved compared to the case where knowledge of the active backhaul links is unavailable.

Reconfigurable intelligent surfaces (RISs) represent a new technology that can shape the radio wave propagation in wireless networks and offers a great variety of possible performance and implementation gains. Motivated by this, we study the achievable rate optimization for multi-stream multiple-input multiple-output (MIMO) systems equipped with an RIS, and formulate a joint optimization problem of the covariance matrix of the transmitted signal and the RIS elements. To solve this problem, we propose an iterative optimization algorithm that is based on the projected gradient method (PGM). We derive the step size that guarantees the convergence of the proposed algorithm and we define a backtracking line search to improve its convergence rate. Furthermore, we introduce the total free space path loss (FSPL) ratio of the indirect and direct links as a first-order measure of the applicability of RISs in the considered communication system. Simulation results show that the proposed PGM achieves the same achievable rate as a state-of-the-art benchmark scheme, but with a significantly lower computational complexity. In addition, we demonstrate that the RIS application is particularly suitable to increase the achievable rate in indoor environments, as even a small number of RIS elements can provide a substantial achievable rate gain.

In this paper, we apply the long short-term memory (LSTM), an advanced recurrent neural network based machine learning (ML) technique, to the problem of transmitter selection (TS) for secrecy in an underlay small-cell cognitive radio network with unreliable backhaul connections. The cognitive communication scenario under consideration has a secondary small-cell network that shares the same spectrum of the primary network with an agreement to always maintain a desired outage probability constraint in the primary network. Due to the interference from the secondary transmitter common to all primary transmissions, the secrecy rates for the different transmitters are correlated. LSTM exploits this correlation and matches the performance of the conventional technique when the number of transmitters is small. As the number grows, the performance degrades in the same manner as other ML techniques such as support vector machine, k-nearest neighbors, naive Bayes, and deep neural network. However, LSTM still significantly outperforms these techniques in misclassification ratio and secrecy outage probability. It also reduces the feedback overhead against conventional TS.

Non-orthogonal multiple access (NOMA) has drawn tremendous attention, being a potential candidate for the spectrum access technology for the fifth-generation (5G) and beyond 5G(B5G) wireless communications standards. Most research related to NOMA focuses on the system performance from Shannon's capacity perspective, which, although a critical system design criterion, fails to quantity the effect of delay constraints imposed by future wireless applications. In this paper, we analyze the performance of a single-input multiple-output (SIMO) two-user downlink NOMA system, in terms of the link-layer achievable rate, known as effective capacity (EC), which captures the performance of the system under a delay-limited quality-of-service (QoS) constraint. For signal combining at the receiver side, we use generalized selection combining (GSC), which bridges the performance gap between the two conventional diversity combining schemes, namely selection combining (SC) and maximal-ratio combining (MRC). We also derive two approximate expressions for the EC of NOMA-GSC which are accurate at low-SNR and at high-SNR, respectively. The analysis reveals a tradeoff between the number of implemented receiver radio-frequency (RF) chains and the achieved performance, and can be used to determine the appropriate number of paths to combine in a practical receiver design.

5G communication systems and beyond are envisioned to support an extremely diverse set of use cases with different performance requirements. These different requirements necessitate the use of different numerologies for increased flexibility. Non-orthogonal multiple access (NOMA) can potentially attain this flexibility by superimposing user signals while offering improved spectral efficiency (SE). However, users with different numerologies have different symbol durations. When combined with NOMA, this changes the nature of the interference the users impose on each other. This paper investigates a multinumerology NOMA (MN-NOMA) scheme using successive interference cancellation (SIC) as an enabler for coexistence of users with with different numerologies. Analytical expressions for the inter-numerology interference (INI) experienced by each user at the receiver are derived, where mean-squared error (MSE) is the metric used to quantity INI. Using the MSE expressions, we analytically derive achievable rates for each user in the MN-NOMA system. These expressions are then evaluated and used to compare the SE performance of MN-NOMA with that of its single-numerology counterpart. The proposed scheme can achieve the desired flexibility in supporting diverse use cases in future wireless networks. The scheme also gains the SE benefits of NOMA compared to both multinumerology and single numerology orthogonal multiple access (OMA) schemes.

Indoor millimeter-wave (mmWave) environment channels are typically sparsely-scattered and dominated by a strong line-of-sight (LOS) path. Therefore, communication over such channels is in general extremely difficult when the LOS path is not present. However, the recent introduction of reconfigurable intelligent surfaces (RISs), which have the potential to influence the propagation environment in a controlled manner, has the potential to change the previous paradigm. Motivated by this, we study the channel capacity optimization utilizing RISs in indoor mmWave environments where no LOS path is present. More precisely, we propose two optimization schemes that exploit the customizing capabilities of the RIS reflection elements in order to maximize the channel capacity. The first optimization scheme exploits only the adjustability of the RIS reflection elements; for this scheme we derive an approximate expression which explains the connection between the channel capacity gains and the system parameters. The second optimization scheme jointly optimizes the RIS reflection elements and the transmit phase precoder; for this scheme, we propose a low-complexity technique called global co-phasing to determine the phase shift values for use at the RIS. Simulation results show that the optimization of the RIS reflection elements produces a significant channel capacity gain, and that this gain increases with the number of RIS elements.

Ultra-reliable and low-latency communication (URLLC) is one of the key applications in fifth generation (5G) cellular networks, which requires extremely high reliability (~99.9999%) and low latency (<; 1 ms). In this paper, the energy efficiency (EE) of multi-user multicarrier amplify-and-forward (AF) networks is maximized under short packet transmission. Accordingly, we formulate an energy-efficient resource allocation problem to jointly optimize the transmit power, subcarrier pairing and allocation, and error probability with finite block-length codes subject to the constraints of the decoding error probability of each user pair, subcarrier pairing and allocation and total transmission power. The formulated problem is non-convex and hence difficult to solve. We analyze the structure of the problem and hence convert it into a convex problem which is approximately equivalent to the original one. An efficient algorithm is also proposed which is capable of producing a near-optimal solution. Simulation results validate the effectiveness of the proposed algorithm that supports energy-efficient URLLC, by showing the impact of various system parameters on EE.

Carrier frequency offset (CFO) can significantly influence the performance of multiple-input multiple-output (MIMO) systems if not estimated and corrected. Most of the existing synchronization techniques are designed for MIMO systems with collocated antennas, where the same frequency error is experienced by the received signal at each antenna. In contrast, for MIMO systems with distributed antennas, the received signals at different receive antennas suffer from different frequency errors. This makes synchronization of such systems computationally complex, especially as the number of receive antennas grows large, i.e. massive MIMO. In this paper, we study the problem of CFO estimation for distributed massive MIMO and cell-free massive MIMO. In particular, we evaluate the performance of distributed large-scale MIMO systems with both collaborative and non-collaborative CFO estimation techniques based on the maximum likelihood (ML) criterion. These optimal CFO estimation results can then serve as benchmarks on the achievable estimation performance of practical collaborative and non-collaborative CFO estimation techniques for distributed MIMO systems. The proposed ML-based CFO estimation methods are tailored to work with periodic pilot sequences. We also show how exploiting the relationships which exist between the CFOs to be estimated can substantially reduce the computational load of CFO estimation in the collaborative approach.

In orthogonal time frequency space (OTFS) systems, channel estimation (CE) is often performed using a pilot based approach. This is usually done in two steps: first, valid channel paths are detected by comparing the magnitude of received symbols against a threshold, and then the associated channel coefficient is estimated. In an attempt to avoid channel path misdetection, existing approaches often deploy large guard bands surrounding a relatively high-power pilot symbol. Furthermore, it is generally assumed that this guard region is sufficiently large to ensure that the time/frequency spreading of the channel does not result in any interference between the pilot and data symbols, thus facilitating simple channel estimation schemes. In this paper, we propose a channel estimation scheme which works even when this assumption is no longer true, i.e., when the channel results in pilot-data interference as may occur in scenarios involving high mobility and/or large delay-spread. The ability of a receiver to operate in such scenarios allows system designers the freedom to use smaller guard bands based on typical (not worst-case) channel spread parameters, thereby yielding higher spectral efficiency. In this work, we derive a maximum likelihood channel path detection scheme followed by a minimum mean-square error channel estimator. The performance advantage of the proposed receiver is verified using extensive bit error rate simulations.

One of the key applications in the fifth generation (5G) communication systems is to support extremely high reliability (~ 99.999%) and low latency (<; 1 ms), namely ultra-reliable and low-latency communication. In this paper, we consider the problem of maximizing energy efficiency (EE) for downlink multi-user multiple-input single-output (MISO) networks under short packet transmission. An optimization problem is formulated to jointly optimize the precoders at the base station (BS) for serving multiple downlink users and the error probability with finite blocklength (FBL) codes, subject to the constraints on decoding error probability per URLLC user and on the BS transmit power. Since the formulated problem is non-convex, we convert this problem into a convex one by analyzing the structure of the EE objective. We then propose an algorithm to find a near-optimal solution for maximizing the EE. Simulation results validate the effectiveness of the proposed algorithm that supports energy-efficient URLLC.

In this paper, we jointly optimize the transceiver design and decoding error probability of a full-duplex (FD) ultrareliable low-latency communication (URLLC) system, where the base-station (BS) operates in an FD mode while the uplink (UL) and downlink (DL) users work in a half-duplex (HD) mode. Accordingly, an optimization problem is formulated for an FD URLLC system under the finite blocklength (FBL) to maximize the achievable total (UL plus DL) rate subject to the reliability (i.e., the decoding error probability) of each link and total transmission power constraints at the UL user and the BS. We convexify the formulated non-convex problem by analyzing the problem structure. Next, an efficient iterative algorithm is proposed to find the near-optimal power allocation for the UL user and the transceiver weights for the BS. Simulation examples show the impact of the blocklength and decoding error probability on the system performance.

Massive multiple‐input multiple‐output (MIMO) is currently entering the practical implementation phase, and key implementation issues for this technology have yet to be fully addressed. Crucial among these is the practical problem of frequency synchronisation, which refers to the adjustment of the clock frequency of local nodes to the clock frequency of a reference node by estimating and compensating carrier frequency offset. Existing theoretical studies on massive MIMO generally assume perfect frequency synchronisation; however, the potentially very high complexity of this process poses a major challenge for massive MIMO systems. Therefore, new frequency synchronisation techniques are urgently needed to make the practical implementation of massive MIMO feasible. In this study, the authors provide a comprehensive classification of the existing research efforts along this line, considering different antenna architectures and modulation schemes. They also highlight the key challenges in frequency synchronisation for massive MIMO, and they outline future research directions on this topic.

Non-orthogonal multiple access (NOMA) is widely recognized as a potential multiple access technology for efficient radio spectrum utilization in the fifth-generation (5G) wireless communications standard. In this paper, we study the average achievable rate and outage probability of a cooperative relaying system (CRS) based on NOMA (CRS-NOMA) over wireless links governed by the α-μ generalized fading model; here α and μ designate the nonlinearity and clustering parameters, respectively, of each link. The average achievable rate is represented in closed-form using Meijer's G-function and the extended generalized bivariate Fox's H-function (EGBFHF), and the outage probability is represented using the lower incomplete Gamma function. Our results confirm that the CRS-NOMA outperforms the CRS with conventional orthogonal multiple access (CRS-OMA) in terms of spectral efficiency at high transmit signal-to-noise ratio (SNR). It is also evident from our results that with an increase in the value of the nonlinearity/clustering parameter, the SNR at which the CRS-NOMA outperforms its OMA based counterpart becomes higher. Furthermore, the asymptotic analysis of the outage probability reveals the dependency of the diversity order of each symbol in the CRS-NOMA system on the α and μ parameters of the fading links.

Multiple-input multiple-output (MIMO) millimeter wave (mmWave) communication is a key technology for next generation wireless networks. As the number of antennas becomes larger and the transmission bandwidth becomes wider, the array steering vectors would vary at different subcarriers, causing the beam squint effect. In this case, the conventional channel model is no longer applicable, especially for the mmWave massive MIMO system. In this paper, we first explain the influence of the beam squint effect from the array signal processing perspective and then investigate the angle-delay sparsity of mmWave transmission. We next design a compressive sensing (CS) algorithm based on shift-invariant block-sparsity that can jointly compute the off-grid angles, the off-grid delays, and the complex gains of the multi-path channel. Compared to either the conventional channel model, or the existing on-grid algorithms, the proposed one more accurately reflects the mmWave channel and is shown to yield better performance of uplink channel estimation.

In this paper, we present a system that performs joint channel coding and constellation shaping for physical-layer network coding (PNC) with quadrature amplitude modulation (QAM). Traditional bit-level PNC (based on the exclusive-OR) has been shown to be effective in increasing the system throughput, but requires a specific design of PNC mapping and shaping code when used with non-binary modulation in order to avoid ambiguity in bit-level detection. We show that PNC applied at symbol level does not present any ambiguity for QAM modulation, so that a wider range of PNC mapping and shaping code designs are possible. Furthermore, we show that the symbol-level PNC approach ensures a shaped signal transmission in both communication phases even with a simple denoising operation at the relay. The simplicity of this denoising operation also facilitates an achievable rate analysis, which is used in the design of shaping codes. Simulation results demonstrate that for end-to-end communication in a PNC system with 16-QAM, the proposed approach achieves a shaping gain of 0.75 dB at a bit error rate of 10-4with a low-complexity (4, 2) shaping block code.

We propose a novel scheme for downlink multiuser multiple-input multiple-output (MIMO) systems, called dual-layered transmit-receive generalized spatial modulation (DL-TR-GSM). The proposed scheme is based on the concept of dual-layered transmission (DLT) which uses two receive antenna power levels instead of receive antenna activation/inactivation to transmit data in the receive spatial domain. Hence, in order to minimize the bit error rate (BER) for DL-TR-GSM, the optimal ratio between the two power levels is determined. To further characterize DL-TR-GSM, we fully derive the computational complexity and show a significant computational complexity reduction as well as a required hardware complexity reduction of DL-TR-GSM, compared to a state-of-the-art benchmark scheme. Simulation results confirm the performance advantages of DL-TR-GSM.

In this paper, we present the error performance analysis of a multiple-input multiple-output (MIMO) physical-layer network coding (PNC) system with two different user-antenna selection (AS) schemes in asymmetric channel conditions. For the first antenna selection scheme (AS1), where the user antenna is selected in order to maximize the overall channel gain between the user and the relay, we give an explicit analytical proof that for binary modulations, the system achieves full diversity order of min(NA, NB) × NRin the multiple-access (MA) phase, where NA, NB, and NRdenote the number of antennas at user A, user B, and relay R, respectively. We present a detailed investigation of the diversity order for the MIMO-PNC system with AS1 in the MA phase for any modulation order. A tight closed-form upper bound on the average SER is also derived for the special case when NR= 1, which is valid for any modulation order. We show that in this case, the system fails to achieve transmit diversity in the MA phase, as the system diversity order drops to 1 irrespective of the number of transmit antennas at the user nodes. Additionally, we propose a Euclidean distance (ED) based user-antenna selection scheme (AS2) that outperforms the first scheme in terms of error performance. Moreover, by deriving upper and lower bounds on the diversity order for the MIMO-PNC system with AS2, we show that this system enjoys both transmit and receive diversity, achieving full diversity order of min(NA, NB) × NRin the MA phase for any modulation order. Monte Carlo simulations are provided which confirm the correctness of the derived analytical results.

Non-orthogonal multiple access (NOMA) and spectrum sharing (SS) are two emerging multiple access technologies for efficient spectrum utilization in future wireless communications standards. In this paper, we present the performance analysis of a NOMA-based cooperative relaying system (CRS) in an underlay spectrum sharing scenario, considering a peak interference constraint (PIC), where the peak interference inflicted by the secondary (unlicensed) network on the primary-user (licensed) receiver (PU-Rx) should be less than a predetermined threshold. In the proposed system the relay and the secondary-user receiver (SU-Rx) are equipped with multiple receive antennas and apply selection combining (SC), where the antenna with highest instantaneous signal-to-noise ratio (SNR) is selected, and maximal-ratio combining (MRC), for signal reception. Closed-form expressions are derived for the average achievable rate and outage probabilities for SS-based CRS-NOMA. These results show that for large values of peak interference power, the SS-based CRS-NOMA outperforms the CRS with conventional orthogonal multiple access (OMA) in terms of spectral efficiency. The effect of the interference channel on the system performance is also discussed, and in particular, it is shown that the interference channel between the secondary-user transmitter (SU-Tx) and the PU-Rx has a more severe effect on the average achievable rate as compared to that between the relay and the PU-Rx. A close agreement between the analytical and numerical results confirm the correctness of our rate and outage analysis.

The next-generation wireless networks are expected to become denser and more heterogeneous in order to boost the network capacity. However, densely deployed base stations (BSs) in heterogeneous networks (HetNets) can give rise to interference. On the other hand, a limited number of channels is allocated within the HetNets. Therefore, the efficient assignment of channels among BSs is considered to be an important issue. Furthermore, the density and heterogeneity of the networks motivate self-organizing resource management techniques. In this paper, we address the problem of channel allocation in HetNets, and propose a satisfaction based channel allocation algorithm. The problem is modeled as a game in satisfaction form, in which BSs act as the players with the constraint given by the loads at the BSs. The objective is to meet the data rate requirements of user equipments. In this regard, the BSs aim at seeking a satisfaction solution rather than the optimal one. In order to learn the satisfaction equilibrium, a fully distributed algorithm based on the individual utility is applied. Simulation results show that the proposed approach can increase the average BS's throughput compared to the benchmark algorithms.

In this paper, an efficient approach for weighted sum rate maximization (WSRMax) for zero-forcing (ZF) methods with general linear transmit covariance constraints (LTCCs) is proposed. This problem has been extensively studied separately for some special cases such as for sum power or per-antenna power constraint (PAPC). Due to some practical and regulatory requirements, these power constraints alone are not in general sufficient, which motivates the consideration of general LTCCs. On the other hand, the zero-forcing (ZF) is a simple linear precoding technique to mitigate inter-user interference. The problem of WSRMax for ZF methods with LTCCs was studied previously using a gradient descent algorithm with barrier functions, but this method was also shown to converge slowly. To derive an efficient solution to this problem, we first reformulate it as an equivalent minimax problem using Lagrangian duality. The obtained result in fact resembles BC-MAC duality but is specialized for ZF methods. We then combine alternating optimization and concave-convex procedure to efficiently compute a saddle point of the minimax problem. The proposed method is numerically shown to converge very fast and its complexity scales linearly with the number of users.

This paper presents a generic foreground calibration algorithm which compensates for memoryless nonlinear impairments in pipeline, SAR or hybrid ADC architectures. Amplifier nonlinearity, comparator offsets, capacitance mismatch and settling time errors are considered. During the calibration process, each element of a look up table is computed by mapping each raw ADC output value to an estimate of the corresponding input, and the most likely input corresponding to each raw ADC output is computed and stored in the table; this table is then used during normal operation to map the raw values to the calibrated ADC outputs. Complexity reduction techniques are presented to facilitate an in-circuit hardware implementation in order to reduce foreground calibration time. The algorithm's performance is evaluated using a SAR ADC model suffering from various nonlinear impairments. Results are presented for settling time errors, capacitor mismatch scenarios, and a wide range of nonlinear amplifier parameters, demonstrating a significant performance improvement in all cases.

This paper presents an efficient approach to computing the capacity of multiple-input multiple-output (MIMO) channels under multiple linear transmit covariance constraints (LTCCs). LTCCs are general enough to include several special types of power constraints as special cases such as the sum power constraint (SPC), per-antenna power constraint (PAPC), or a combination thereof. Despite its importance and generality, most of the existing literature considers either SPC or PAPC independently. Efficient solutions to the computation of the MIMO capacity with a combination of SPC and PAPC have been recently reported, but were only dedicated to multiple-input single-output (MISO) systems. For the general case of LTCCs, we propose a low-complexity semi-closed-form approach to the computation of the MIMO capacity. Specifically, a modified minimax duality is first invoked to transform the considered problem in the broadcast channel into an equivalent minimax problem in the dual multiple access channel. Then alternating optimization and concave-convex procedure are utilized to derive water-filling-based algorithms to find a saddle point of the minimax problem. This is different from the state-of-the-art solutions to the considered problem, which are based on interior-point or subgradient methods. Analytical and numerical results are provided to demonstrate the effectiveness of the proposed low-complexity solution under various MIMO scenarios.

This paper investigates the outage probability of the achievable secrecy rate in the presence of multiple eavesdroppers that employ energy harvesting (EH) and information decoding (ID). We derive the theoretical outage probability of the achievable secrecy rate between the legitimate transmitter and receiver pair when both the main channel and wiretap channel experience Rician fading. This work also considers both ideal and imperfect channel state information as well as different EH architectures (i.e. separated and integrated receiver architecture) in the secrecy analysis. Furthermore, the use of transmit antenna selection (TAS) for enhancing message confidentiality is also studied. Numerical and simulation results are provided to validate our analysis.

Spatial modulation, a multiple-input multiple-output (MIMO) technology which uses the antenna index as an additional means of conveying information, is an emerging technology for modern wireless communications. In this paper, a new distributed version of spatial modulation is proposed which achieves virtual full-duplex communication (VFD-DSM), allowing the source to transmit new data while the relay set forwards the source's data in every time slot. Two maximum a posteriori (MAP) detection methods at the destination are proposed for this VFD-DSM protocol: one, called local MAP, is based on processing the signals received over each pair of consecutive time slots, while the other, called global MAP, is based on symbol-error-rate optimal detection over an entire frame of data. Simulation results for the proposed VFD-DSM protocol indicate that for source data detection at high signal-to-noise ratio (SNR), VFD-DSM with local MAP detection can provide a similar error rate performance to that of successive relaying, while providing a significant throughput advantage since the relays can forward the source transmissions while also transmitting their own data. Furthermore, the use of global MAP detection is shown to yield a further 1.8 dB improvement in source data error rate while still maintaining this throughput advantage.

The distributed spatial modulation (DSM) protocol, which allows relays to forward the source's data while simultaneously allowing the relays to transmit their own data, has been proposed by Narayanan et al. In this paper, we introduce two new protocols for enabling the DSM, consisting of single-antenna network nodes, with simultaneous wireless information and power transfer capability: power splitting-based DSM (PS-DSM) and energy recycling-based DSM (ER-DSM). More specifically, the PS-DSM relies on power splitters at the relay nodes to harvest energy transmitted from the source. On the other hand, the ER-DSM, by exploiting the inactive cooperating relays in DSM-based protocols, recycles part of the transmitted energy in the network, without relying on power splitters or time switches at the relays to harvest energy. This leads to an increase in the average harvested energy at the relays with reduced hardware complexity. Both the PS-DSM and the ER-DSM also retain all the original features of DSM. Due to its particular operating principle and specific advantages, we select the ER-DSM as the candidate for further mathematical analysis. More specifically, by considering a multi-state battery model, we propose an analytical framework based on a Markov chain formulation for modeling the charging/discharging behavior of the batteries at the relay nodes in the ER-DSM. Furthermore, based on the derived Markov chain model, we introduce a mathematical framework for computing the error probability of the ER-DSM, by explicitly taking into account, the effect of finite-sized batteries. The frameworks are substantiated with the aid of Monte Carlo simulations for various system setups.

The recently proposed multiple-input multiple-output (MIMO) technique of spatial modulation (SM) has attracted a good deal of attention due to its low implementation and computational complexity, and the spectral efficiency and energy efficiency gains it offers over many conventional MIMO schemes. There has been some progress made in applying SM to multiuser scenarios, including a proposed precoding scheme to eliminate the Multiuser Interference (MUI) associated with multiuser environments. A generalized technique for SM has also been proposed that promises further spectral efficiency gains over conventional SM. This paper proposes a precoding scheme to eliminate MUI in a generalized spatial modulation (GSM) scenario, thereby allowing individual users to employ a singleuser Maximum Likelihood optimum detector. An interference-aware multiuser detection scheme is developed and the performance of both schemes is compared. The effect of precoder power normalization on the error rate performance is also explored in detail. Precoding is found to facilitate less complex detection and superior error rate performance in the multiuser GSM context.

Physical-layer network coding (PNC) is now well- known as a potential candidate for delay-sensitive and spectrally efficient communication applications, especially in two-way relay channels (TWRCs). In this paper, we present the error performance analysis of a multiple-input single- output (MISO) fixed network coding (FNC) system with two different transmit antenna selection (TAS) schemes. For the first scheme, where the antenna selection is performed based on the strongest channel, we derive a tight closed-form upper bound on the average symbol error rate (SER) with M-ary modulation and show that the system achieves a diversity order of 1 for M > 2. Next, we propose a Euclidean distance (ED) based antenna selection scheme which outperforms the first scheme in terms of error performance and is shown to achieve a diversity order lower bounded by the minimum of the number of antennas at the two users.

In this paper, we present a low-density parity-check coded modulation approach addressing orthogonal modulations with moderate order (between 8 and 32) over the additive white Gaussian noise channel. The proposed design is based on a constrained optimization of a non-binary low-density parity-check ensemble degree distribution, where the iterative decoding threshold is optimized via extrinsic information transfer analysis while restricting the search to degree distributions that target low error floors. For various orthogonal modulation orders, we provide useful approximations to the extrinsic information transfer functions, which enable a fast optimization with respect to the iterative decoding threshold. The approach is validated via codeword error rate Monte Carlo simulations and complemented by an error floor analysis, showing gains up to 0.8 dB at a codeword error rate of 10-4with respect to existing designs, down to information block lengths as short as 192 bits.

This paper presents a technique to estimate the time skew in time-interleaved ADCs. The proposed method estimates all of the time skew parameters jointly based on observations from a bank of correlators. The proposed method works for an arbitrary number of sub-ADCs. For implementation of the correlator bank, we propose the use of Mitchell's logarithmic multiplier and a hardware reuse mechanism, thereby reducing the complexity and power consumption. Also, we explain why blind estimation techniques alone (including the proposed one) are not always sufficient for time skew estimation for certain classes of input signal; for the proposed approach, however, a simple modification to the analogue circuit (suitable for SAR ADCs) is shown to successfully deal with such problems, with only a minor penalty in power and area. The technique is verified by extensive simulations including a spectrally rich input signal in which an MTPR (multi-tone power ratio) improvement from 29dB to 62dB was achieved for a TIADC system having 16 sub-ADCs.

Efficient heterogeneous communication technologies are critical components to provide flawless connectivity in smart cities. The proliferation of wireless technologies, services and communication devices has created the need for green and spectrally efficient communication technologies. Physical-layer network coding (PNC) is now well-known as a potential candidate for delay-sensitive and spectrally efficient communication applications, especially in bidirectional relaying, and is therefore well-suited for smart city applications. In this paper, we provide a brief introduction to PNC and the associated distance shortening phenomenon which occurs at the relay. We discuss the issues with existing schemes that mitigate the deleterious effect of distance shortening, and we propose simple and effective solutions based on the use of multiple antenna systems. Simulation results confirm that full diversity order can be achieved in a PNC system by using antenna selection schemes based on the Euclidean distance metric.

In this paper, we investigate, for the first time, the performance of a full-duplex (FD) relaying protocol, where a single-RF spatial modulation (SM) multiple-input multiple-output (MIMO) system is employed at the relay node. We refer to this protocol as SM-aided FD relaying (SM-FDR). At the destination, a demodulator that takes advantage of the direct connectivity between the source and destination is developed in order to maximize its performance. Based on this demodulator, we introduce a mathematical framework for computing the average error-probability of SM-FDR in the presence of residual self-interference (SI). Furthermore, we derive mathematical expressions for computing the achievable rate of SM-FDR. With the aid of these achievable rate expressions, we provide an estimate on the quality of SI cancellation required for the suitability of FD transmission. In addition, we develop and evaluate three relay selection policies specifically designed for the SM-FDR protocol. The mathematical analysis is substantiated with the aid of extensive Monte Carlo simulations. Finally, we also assess the performance of SM-FDR against traditional FD relaying protocols.

Spatial modulation, a multiple-input multiple-output (MIMO) technology which uses the antenna index to transmit part of the incoming data, is an attractive way to reduce the energy cost and transceiver complexity in future wireless networks. In particular, the recently proposed technique of distributed spatial modulation (DSM) for relay networks can lead to better spectral efficiency, as it allows the relays to transmit their own data while simultaneously relaying the data of the source. A new distributed spatial modulation protocol is introduced in this paper which achieves virtual full duplex (VFD) communication. In this protocol, the source and relays transmit their own data in every time slot; thus, the spectral efficiency is significantly improved compared to conventional DSM. Simulation results indicate that at high signal-to-noise ratio (SNR), the proposed protocol has similar bit error rate (BER) performance versus SNR-per-bit compared to the standard full duplex relaying protocol of successive relaying; however, in contrast to successive relaying, the relays are simultaneously transmitting their own data, which is received at the destination with an error rate similar to that of the source's data.

A new joint message-passing decoder is presented for use in a two-user cooperative wireless network. This decoder is designed for use with the diversity network coding scheme of Xiao et al. , which uses nonbinary network codes together with channel coding to achieve high diversity gains. The proposed joint decoder, together with appropriate modifications to the cooperative protocol of Xiao and Skoglund (2010), significantly reduces the required implementation complexity both at the relay nodes and at the receiver. The destination's joint decoder structure consists of two parallel weighted bit flipping (PWBF) decoders which exchange extrinsic soft/hard information regarding the two users' packets. It is demonstrated through simulations that the proposed joint decoder achieves not only the same diversity gain as in the work of Xiao and Skoglund (2010), but also approximately 5dB of additional coding gain. It is also notable that a significant improvement in system performance can be achieved after only two joint decoding iterations.

Low-density lattice codes (LDLCs) are known for their high decoding efficiency and near-capacity performance on point-to-point Gaussian channels. In this paper, we present a distributed LDLC-based cooperative relaying scheme for the multiple-access relay channel (MARC). The relay node decodes LDLC-coded packets from two sources and forwards a network-coded combination to the destination. At the destination, a joint iterative decoding structure is designed to exploit the diversity gain as well as coding gain. For the LDLC-based network coding operation at the relay, we consider two alternative methods which offer a tradeoff between implementation complexity and performance, called superposition LDLC (S-LDLC) and modulo-addition LDLC (MA-LDLC). Soft symbol relaying is considered as an alternative to hard decision relaying which is capable of reducing the effect of error propagation at the relay. Simulation results show that the proposed scheme can provide greater diversity gain and up to 6.2 dB coding gain when compared with noncooperative LDLC coding and uncoded network-coded transmission. The proposed scheme also achieves 2.5 dB gain over network-turbo-coded cooperation, for the same code rate and overall transmitted power. Also, soft symbol relaying is shown to provide approximately 2 dB gain over hard decision relaying when the source-relay link suffers from deep fading.

This paper proposes the novel technique of multilevel threshold based soft quantization (MLT-SQ) for a multiple access relay system (MARS). The scheme is suitable for systems using binary phase-shift keying (BPSK) and network coding at the relay. In the proposed MLT-SQ protocol, the relay evaluates the reliabilities, expressed as log-likelihood ratios (LLRs), of the received signals from the two sources. It then computes the LLRs of the network-coded packet and quantizes these using a set of optimized multilevel thresholds, forwarding the resulting “quantized soft symbols” to the destination. We provide the derivation for the bit error rate (BER) at the destination, based on which we optimize the multilevel thresholds to minimize the BER. Compared to competing schemes, the performance of our system is superior in terms of BER when the same amount of channel state information (CSI) is exploited.

This paper investigates a low-density parity-check (LDPC) coded soft-decode-and-forward (SDF) relaying protocol for a two way relay channel (TWRC). In this SDF protocol, the relay evaluates the reliabilities, expressed as log-likelihood ratios (LLRs), of the received signals from the two sources. The relay then forwards a network-coded combination of the parity symbols of both sources, but in the “soft” domain to avoid error propagation from the relay. We introduce a model for the effective noise experienced by the soft network coded symbols, constituting the new parameters of soft scalar and soft error; this model is then used to compute the log-likelihood ratios (LLRs) at the destination. To facilitate this latter computation, we have derived an analytical expression for soft error variance, as well as a simplified expression based on a common assumption on the statistical behavior of the LLRs. This enables low-complexity computation and tracking of the soft error variance on-the-fly. The proposed system outperforms standard competing schemes reported in the literature in terms of error rate performance over Rayleigh fading links.

In this paper, the minimum distance distribution of irregular generalized LDPC (GLDPC) code ensembles is investigated. Two classes of GLDPC code ensembles are analyzed; in one case, the Tanner graph is regular from the variable node perspective, and in the other case the Tanner graph is completely unstructured and irregular. In particular, for the former ensemble class we determine exactly which ensembles have minimum distance growing linearly with the block length with probability approaching unity with increasing block length. This work extends previous results concerning LDPC and regular GLDPC codes to the case where a hybrid mixture of check node types is used.

This paper investigates soft information relaying (SIR) for low-density parity-check (LDPC) coded transmission in wireless networks. We introduce a new scheme for soft parity symbol generation at the relay, which features two key strategies: a two-step soft parity generation process, and a prescaling technique. The two-step soft parity generation procedure is designed to allow efficient relay processing, while yielding an overall (i.e., destination) parity-check matrix structure with desirable properties. The pre-scaling method prevents the amplitudes of generated soft symbols successively converging to zero, as happens with some existing soft forwarding methods. Finally, we propose an appropriate LLR former at the destination which is tailored to the proposed soft parity generation technique. Simulation results demonstrate that the proposed relay protocol yields an improved BER performance compared to competitive schemes proposed in the literature.

Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes has attracted much attention in the research community in the past few years. LP decoding has been derived for binary and nonbinary linear codes. However, the most important problem with LP decoding for both binary and nonbinary linear codes is that the complexity of standard LP solvers such as the simplex algorithm remains prohibitively large for codes of moderate to large block length. To address this problem, two low-complexity LP (LCLP) decoding algorithms for binary linear codes have been proposed by Vontobel and Koetter, henceforth called the basic LCLP decoding algorithm and the subgradient LCLP decoding algorithm. In this paper, we generalize these LCLP decoding algorithms to nonbinary linear codes. The computational complexity per iteration of the proposed nonbinary LCLP decoding algorithms scales linearly with the block length of the code. A modified BCJR algorithm for efficient check-node calculations in the nonbinary basic LCLP decoding algorithm is also proposed, which has complexity linear in the check node degree. Several simulation results are presented for nonbinary LDPC codes defined over Z4, GF(4), and GF(8) using quaternary phase-shift keying and 8-phase-shift keying, respectively, over the AWGN channel. It is shown that for some group-structured LDPC codes, the error-correcting performance of the nonbinary LCLP decoding algorithms is similar to or better than that of the min-sum decoding algorithm.

This paper analyzes the asymptotic exponent of the weight spectrum for irregular doubly-generalized LDPC (D-GLDPC) codes. In the process, an efficient numerical technique for its evaluation is presented, involving the solution of a 4 × 4 system of polynomial equations. The expression is consistent with previous results, including the case where the normalized weight or stopping set size tends to zero. The spectral shape is shown to admit a particularly simple form in the special case where all variable nodes are repetition codes of the same degree, a case which includes Tanner codes; for this case it is also shown how certain symmetry properties of the local weight distribution at the CNs induce a symmetry in the overall weight spectral shape function. Finally, using these new results, weight and stopping set size spectral shapes are evaluated for some example generalized and doubly-generalized LDPC code ensembles.

In a recent paper, a method was proposed to accelerate the majority logic decoding of difference set low density parity check codes. This is useful as majority logic decoding can be implemented serially with simple hardware but requires a large decoding time. For memory applications, this increases the memory access time. The method detects whether a word has errors in the first iterations of majority logic decoding, and when there are no errors the decoding ends without completing the rest of the iterations. Since most words in a memory will be error-free, the average decoding time is greatly reduced. In this brief, we study the application of a similar technique to a class of Euclidean geometry low density parity check (EG-LDPC) codes that are one step majority logic decodable. The results obtained show that the method is also effective for EG-LDPC codes. Extensive simulation results are given to accurately estimate the probability of error detection for different code sizes and numbers of errors.

For a binary linear code, the pseudocodeword redundancy with respect to the additive white Gaussian noise channel, the binary symmetric channel, or the max-fractional weight is defined to be the smallest number of rows in a parity-check matrix such that the corresponding minimum pseudoweight is equal to the minimum Hamming distance of the code. It is shown that most codes do not have a finite pseudocodeword redundancy. Also, upper bounds on the pseudocodeword redundancy for some families of codes, including codes based on designs, are provided. The pseudocodeword redundancies for all codes of small length (at most 9) are computed. Furthermore, comprehensive results are provided on the cases of cyclic codes of length at most 250 for which the eigenvalue bound of Vontobel and Koetter is sharp.

Using the EXIT chart approach, a necessary and sufficient condition is developed for the local stability of iterative decoding of multi-edge type (MET) doubly-generalized low-density parity-check (D-GLDPC) code ensembles. In such code ensembles, the use of arbitrary linear block codes as component codes is combined with the further design of local Tanner graph connectivity through the use of multiple edge types. The stability condition for these code ensembles is shown to be succinctly described in terms of the value of the spectral radius of an appropriately defined polynomial matrix.

Linear Programming (LP) decoding is emerging as an attractive alternative to decode Low-Density Parity-Check (LDPC) codes. However, the earliest LP decoders proposed for binary and nonbinary LDPC codes are not suitable for use at moderate and large code lengths. To overcome this problem, Vontobel et al. developed an iterative Low-Complexity LP (LCLP) decoding algorithm for binary LDPC codes. The variable and check node calculations of binary LCLP decoding algorithm are related to those of binary Belief Propagation (BP). The present authors generalized this work to derive an iterative LCLP decoding algorithm for nonbinary linear codes. Contrary to binary LCLP, the variable and check node calculations of this algorithm are in general different from that of nonbinary BP. The overall complexity of nonbinary LCLP decoding is linear in block length; however the complexity of its check node calculations is exponential in the check node degree. In this paper, we propose a modified BCJR algorithm for efficient check node processing in the nonbinary LCLP decoding algorithm. The proposed algorithm has complexity linear in the check node degree. We also introduce an alternative state metric to improve the run time of the proposed algorithm. Simulation results are presented for (504, 252) and (1008, 504) nonbinary LDPC codes over ℤ4.

It is shown that a large class of communication systems which admit a sum-product algorithm (SPA) based receiver also admit a corresponding linear-programming (LP) based receiver. The two receivers have a relationship defined by the local structure of the underlying graphical model, and are inhibited by the same phenomenon, which we call pseudoconfigurations. This concept is a generalization of the concept of pseudocodewords for linear codes. It is proved that the LP receiver has the `maximum likelihood certificate' property, and that the receiver output is the lowest cost pseudoconfiguration. Equivalence of graph-cover pseudoconfigurations and linear-programming pseudoconfigurations is also proved. A concept of system pseudodistance is defined which generalizes the existing concept of pseudodistance for binary and nonbinary linear codes. It is demonstrated how the LP design technique may be applied to the problem of joint equalization and decoding of coded transmissions over a frequency selective channel, and a simulation-based analysis of the error events of the resulting LP receiver is also provided. For this particular application, the proposed LP receiver is shown to be competitive with other receivers, and to be capable of outperforming turbo equalization in bit and frame error rate performance.

In this paper, the asymptotic growth rate of the weight distribution of irregular doubly generalized LDPC (D-GLDPC) codes is derived. The analysis yields a compact expression which accurately approximates the growth rate function for the case of small linear-weight codewords. This paper generalizes existing results for LDPC and generalized LDPC (GLDPC) codes. Ensembles with smallest check or variable node minimum distance greater than 2 are shown to have good growth-rate behavior, while for other ensembles a fundamental parameter is identified which discriminates between an asymptotically small and an asymptotically large expected number of small linear-weight codewords. Also, in the latter case it is shown that the growth rate depends only on the check and variable nodes with minimum distance 2. An important connection between this new result and the stability condition of D-GLDPC codes over the BEC is highlighted. Such a connection, previously observed for LDPC and GLDPC codes, is now extended to the case of D-GLDPC codes. Finally, it is shown that the analysis may be extended to include the growth rate of the stopping set size distribution of irregular D-GLDPC codes.

This paper analyzes the asymptotic exponent of both the weight spectrum and the stopping set size spectrum for a class of generalized low-density parity-check (GLDPC) codes. Specifically, all variable nodes (VNs) are assumed to have the same degree (regular VN set), while the check node (CN) set is assumed to be composed of a mixture of different linear block codes (hybrid CN set). A simple expression for the exponent (which is also referred to as the growth rate or the spectral shape) is developed. This expression is consistent with previous results, including the case where the normalized weight or stopping set size tends to zero. Furthermore, it is shown how certain symmetry properties of the local weight distribution at the CNs induce a symmetry in the overall weight spectral shape function.

We define the AWGNC, BSC, and max-fractional pseudocodeword redundancy p(C) of a code C as the smallest number of rows in a parity-check matrix such that the corresponding minimum pseudoweight is equal to the minimum Hamming distance of C. We show that most codes do not have a finite p(C). We also provide bounds on the pseudocodeword redundancy for some families of codes, including codes based on designs.

In this paper we propose a cooperative diversity scheme for the communication model of two sources sharing a single relay. The scheme uses algebraic code superposition relaying in the multiple access fading channel to create spatial diversity under the constraint of limited communications resources. We also describe in detail a novel computationally efficient message passing algorithm at the destination's decoder which extracts the substantial spatial diversity contained in the code superposition and signal superposition. The decoder is based on a sliding window structure where certain a posteriori LLRs are retained to form a priori LLRs for the next decoding. We show that despite the simplicity of the proposed scheme, diversity gains are efficiently leveraged by the simple combination of channel coding at the sources and network coding at the relay.

The growth rate of the weight distribution of irregular doubly-generalized LDPC (D-GLDPC) codes is developed and in the process, a new efficient numerical technique for its evaluation is presented. The solution involves simultaneous solution of a 4 × 4 system of polynomial equations. This represents the first efficient numerical technique for exact evaluation of the growth rate, even for LDPC codes. The technique is applied to two example D-GLDPC code ensembles.

In this paper we analyze the bound on the additive white Gaussian noise channel (AWGNC) pseudo-weight of a (c, d)-regular linear block code based on the two largest values ¿1> ¿2of the eigenvalues of HTH: wpmin> (H) ¿ n = 2c-¿2/¿1-¿2. In particular, we analyze (c, d)-regular quasi-cyclic (QC) codes of length rL described by J × L block parity-check matrices with circulant block entries of size r × r. We proceed by showing how the problem of computing the eigenvalues of the rL × rL matrix HTH can be reduced to the problem of computing eigenvalues for r matrices of size L × L. We also give a necessary condition for the bound to be attained for a circulant matrix H and show a few classes of cyclic codes satisfying this criterion.

A class of doubly-generalized low-density parity-check (D-GLDPC) codes, where single parity-check (SPC) codes are used as variable nodes (VNs), is investigated. An expression for the growth rate of the weight distribution of any D-GLDPC ensemble with a uniform check node (CN) set is presented at first, together with an analytical technique for its efficient evaluation. These tools are then used for detailed analysis of a case study, namely, a rate-1/2 D-GLDPC ensemble where all the CNs are (7, 4) Hamming codes and all the VNs are length-7 SPC codes. It is illustrated how the VN representations can heavily affect the code properties and how different VN representations can be combined within the same graph to enhance some of the code parameters. The analysis is conducted over the binary erasure channel. Interesting features of the new codes include the capability of achieving a good compromise between waterfall and error floor performance while preserving graphical regularity, and values of threshold outperforming LDPC counterparts.

Compound precoding is a state-of-the-art technique for combining trellis coding and decision-feedback equalisation (DFE) prior to upstream transmission on the telephone-line channel, and is an option in the International Telecommunications Union (ITU)-T V.92 standard. In this paper, we provide a detailed overview of this technique. We demonstrate that compound precoding combines in a straightforward manner with most practical trellis codes. We show that compound precoding exhibits a signal-to-noise ratio (SNR) gain with respect to other schemes which combine with trellis coding, and quantify this gain. We also show that, for stability of the compound precoder, the precoder feedforward filter must be decomposed into its constituent minimum phase (MP) and all pass (AP) components. Finally, a simulation study of V.92 upstream transmission demonstrates the shaping advantage of compound precoding over competitor techniques for pre-equalisation in this setting.

A framework for linear-programming (LP) decoding of nonbinary linear codes over rings is developed. This framework facilitates LP-based reception for coded modulation systems which use direct modulation mapping of coded symbols. It is proved that the resulting LP decoder has the ldquomaximum-likelihood (ML) certificaterdquo property. It is also shown that the decoder output is the lowest cost pseudocodeword. Equivalence between pseudocodewords of the linear program and pseudocodewords of graph covers is proved. It is also proved that if the modulator-channel combination satisfies a particular symmetry condition, the codeword error rate performance is independent of the transmitted codeword. Two alternative polytopes for use with LP decoding are studied, and it is shown that for many classes of codes these polytopes yield a complexity advantage for decoding. These polytope representations lead to polynomial-time decoders for a wide variety of classical nonbinary linear codes. LP decoding performance is illustrated for ternary Golay code with ternary phase-shift keying (PSK) modulation over additive white Gaussian noise (AWGN), and in this case it is shown that the performance of the LP decoder is comparable to codeword-error-rate-optimum hard-decision-based decoding. LP decoding is also simulated for medium-length ternary and quaternary low-density parity-check (LDPC) codes with corresponding PSK modulations over AWGN.

A coded modulation system is considered in which nonbinary coded symbols are mapped directly to nonbinary modulation signals. It is proved that if the modulator-channel combination satisfies a particular symmetry condition, the codeword error rate performance is independent of the transmitted codeword. It is shown that this result holds for both linear-programming decoders and sum-product decoders. In particular, this provides a natural modulation mapping for nonbinary codes mapped to PSK constellations for transmission over memoryless channels such as AWGN channels or flat fading channels with AWGN.

In previous work, we demonstrated how decoding of a non-binary linear code could be formulated as a linear-programming problem. In this paper, we study different polytopes for use with linear-programming decoding, and show that for many classes of codes these polytopes yield a complexity advantage for decoding. These representations lead to polynomial-time decoders for a wide variety of classical non-binary linear codes.

This paper presents a novel method for constructing low density parity check (LDPC) codes with a girth of up to 8. These codes are based on the structural properties of finite lattices. Results are presented which show that these codes perform well over AWGN channels with iterative decoding.