The escalating storage density of three-dimensional (3D) NAND flash memory introduces heightened channel noise, significantly degrading channel quality and exacerbating the raw bit error rate (RBER). The fixed and unchangeable code rate of the traditional global coupled low-density-parity-check (GC-LDPC) codes fails to address the performance mismatch arising from the stochastic temporal and spatial fluctuations in 3D NAND flash channels. To address the above issue efficiently, in this paper we investigate high-rate-compatible LDPC codes in 3D NAND flash memory. Firstly, we analyze the flash memory channel characteristics from the FPGA test platform and model the 3D triple-level cell (TLC) NAND flash channel. Subsequently, we propose a novel High-Rate-Compatible Algebraic GC-LDPC (HRC-A-GC-LDPC) code and conduct a comprehensive theoretical analysis of its structure and performance. Specifically, the HRC-A-GC-LDPC code features an information bit length of 4 KB and supports dynamic adjustment to multiple code rates, enabling it to match the varying characteristics of 3D NAND flash channels. This paper also examines and analyzes various construction methods for the HRC-A-GC-LDPC code corresponding to different column weights (CWs), providing insights into its design flexibility. Simulation results demonstrate that, in 3D TLC NAND flash memory, the proposed HRC-A-GC-LDPC code outperforms conventional GC-LDPC codes in both error correction capability and extended memory lifetime, validating its suitability for high-density 3D NAND flash applications.

With the continuous improvement of data memory density, as the common solution for error correction of NAND flash, the low-density-parity-check (LDPC) code faces more challenges, such as the increasing code length requirements, the worse raw bit error rates (RBER), and the frequently varied channels. In this paper, a new (37536,33672) spatially coupled and globally coupled LDPC (SC-GC-LDPC) code is constructed to address the above challenge, which outperforms the traditional globally coupled LDPC (GC-LDPC) code with the gaps of 0.065 dB and 0.08 dB by exploiting the layered sum-product algorithm (SPA) and the layered normalized min-sum (NMS) algorithm, respectively. In the flash channel, the SC-GC-LDPC code also shows superior error correction performance than the conventional GC-LDPC codes with 25% improvement. Due to its special structure of the check matrix, an improved two-level decoding algorithm (ITLA) and an improved two-phase decoding algorithm (ITPA) are proposed in this paper. Specifically, the algorithms exploit the adjacent subcodes to correct the faulty ones, which reduces the number of check-node-updating (CNU). For the case of single subcode errors, the simulation results show that the number of CNU is reduced by ranging from 6.64% to 31.14% by applying our proposed algorithms, leading to significant improvement of throughput. Compared with the conventional algorithms, the ITLA and ITPA only show slight performance loss. Moreover, ITPA also provides high flexibility of decoding in the NAND flash memory, which can achieve the balance between the error-correction performance and the throughput.

As the number of stacked layers in 3D NAND flash memory increases, the channels experience more complex noise, leading to significant fluctuations in the error detection rate. Error-correcting codes with varying error correction capabilities (ECC) are required at different flash stages. To address this issue, we investigate multi-high-rate low-density parity-check (LDPC) codes for 3D NAND flash memory in this paper. Firstly, we mathematically model the 3D triple-level cell (TLC) NAND flash channel based on the obtained data from the test platform. Then we propose a multi-high-rate structured algebraic quasi-cyclic LDPC (MHR-SA-QC-LDPC) code. Specifically, the MHR-SA-QC-LDPC code contains the fixed number of information bits and can be adjusted to various rates according to the characteristics of NAND flash channels. Both additive and multiplicative group construction methods are analyzed in the prime field. Simulation results demonstrate that the proposed LDPC codes outperform existing benchmarks in 3D TLC NAND flash channels, improving both ECC performance and device lifetime.

The performance of over-the-air computation (AirComp) systems degrades due to the hostile channel conditions of wireless devices (WDs), which can be significantly improved by the employment of reconfigurable intelligent surfaces (RISs). However, the conventional RISs require that the WDs have to be located in the half-plane of the reflection space, which restricts their potential benefits. To address this issue, the novel family of simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS) is considered in AirComp systems to improve the computation accuracy across a wide coverage area. To minimize the computation mean-squared-error (MSE) in STAR-RIS assisted AirComp systems, we propose a joint beamforming design for optimizing both the transmit power at the WDs, as well as the passive reflect and transmit beamforming matrices at the STAR-RIS, and the receive beamforming vector at the fusion center (FC). Specifically, in the updates of the passive reflect and transmit beamforming matrices, closed-form solutions are derived by introducing an auxiliary variable and exploiting the coupled binary phase-shift conditions. Moreover, by assuming that the number of antennas at the FC and that of elements at the STAR-RIS/RIS are sufficiently high, we theoretically prove that the STAR-RIS assisted AirComp systems provide higher computation accuracy than the conventional RIS assisted systems. Our numerical results show that the proposed beamforming design outperforms the benchmark schemes relying on random phase-shift constraints and the deployment of conventional RIS. Moreover, its performance is close to the lower bound achieved by the beamforming design based on the STAR-RIS dispensing with coupled phase-shift constraints.

Over-the-air computation (AirComp) has been recognized as a promising technique of enabling the fusion center (FC) to aggregate the data gleaned from massive distributed wireless devices (WDs). Nevertheless, the computational performance of AirComp is significantly affected by the potentially poor channel conditions between the WDs and FC due to physical obstacles. For mitigating this limitation, we employ reconfigurable intelligent surfaces (RISs) for enhancing the reception quality and, thus, improve the computational performance of AirComp. Moreover, the previous studies of RIS-assisted AirComp tend to rely on the real-time channel state information (CSI), leading to excessive overhead since the number of RIS elements is large. To mitigate the above issue, a mixed-timescale penalty-dual-decomposition (MTPDD) algorithm is proposed, in which the transmit power of each WD, the receive beamforming vector at the FC, and the passive beamforming matrix of the RIS are jointly optimized. We aim to minimize the average computation mean-squared error (MSE) over time with reduced signaling overhead. Specifically, at each time slot, we optimize the short-term transmit power and receive the beamforming vector based on the real-time low-dimensional CSI vectors. In contrast, in each frame, we update the long-term passive RIS beamforming matrix based on the channel statistics. Besides, we analyzed both the convergence and the computational complexity of the proposed algorithms. Simulation results verify the benefits of our proposed MTPDD beamforming algorithm. It is also shown that the performance of the MTPDD algorithm approaches that achieved by the scheme using real-time perfect CSI with reduced signal overhead.

Over-the-air computation (AirComp) has received substantial attention, given its ability to aggregate massive amounts of data from distributed wireless devices (WDs). However, the computation accuracy at the fusion center (FC) may be severely affected by receiving data corrupted by the poor channel conditions. To mitigate this issue, we consider the employment of reconfigurable intelligent surfaces (RISs) in the AirComp system considered for improving the quality of received data, and hence improve the computation accuracy. However, most previous contributions on RIS-assisted AirComp systems only employ a single RIS in the resultant single-RIS-assisted (SRIS-assisted) AirComp systems. We develop this concept further for mitigating the deleterious channel effects by conceiving a double-RIS-assisted (DRIS-assisted) AirComp system, where one of the RISs is located near the WDs and the other in the vicinity of the FC. We theoretically prove that the DRIS-assisted AirComp system outperforms its SRIS-assisted counterpart in terms of the resultant computation mean-squared-error (MSE). Furthermore, we propose a pair of algorithms for jointly optimizing the transmit power at the WDs, the receive beamforming vector at the FC, and the passive beamforming matrices at the RISs for minimizing the computational MSE. Specifically, the transmit power is updated by exploiting the Lagrange duality method, while the receive beamforming vector is optimized by utilizing the first-order optimality condition. Furthermore, a pair of techniques are developed for optimizing the passive beamforming matrices at the RISs based on semidefinite relaxation (SDR) and penalty-duality-decomposition (PDD), respectively. Both the complexity and the convergence of the proposed algorithms are analyzed. Finally, simulation results are provided for quantifying the overall performance of the resultant DRIS-assisted AirComp system.

Over-the-air computation (AirComp) has been recognized as a promising technique in Internet-of-Things (IoT) networks for fast data aggregation from a large number of wireless devices. However, the computation accuracy of AirComp highly depends on the devices with the worst channels condition, which degrades severely when the number of devices becomes large. To address this issue, we exploit the massive multiple-input multiple-output (MIMO) with hybrid beamforming, in order to enhance the computational accuracy of AirComp in a cost-effective manner. In particular, we consider the scenario with a large number of multi-antenna devices simultaneously sending data to an access point (AP) equipped with massive antennas for functional computation over the air. Under this setup, we jointly optimize the transmit digital beamforming at the wireless devices and the receive hybrid beamforming at the AP, with the objective of minimizing the computational mean-squared error (MSE) subject to the individual transmit power constraints at the wireless devices. To solve the non-convex hybrid beamforming design optimization problem, we propose an alternating-optimization-based approach, in which the transmit digital beamforming and the receive analog and digital beamforming are optimized in an alternating manner. In particular, we propose two computationally efficient algorithms to handle the challenging receive analog beamforming problem, by exploiting the techniques of successive convex approximation (SCA) and coordinate descent (CD), respectively. It is shown that for the special case with a fully-digital receiver at the AP, the achieved MSE of the massive MIMO AirComp system is inversely proportional to the number of receive antennas. Furthermore, numerical results show that the proposed hybrid beamforming design substantially enhances the computation MSE performance as compared to other benchmark schemes, while the SCA-based algorithm performs closely to the performance upper bound achieved by the fully-digital beamforming.

In this article, we propose a sparse hybrid combining (SHC) scheme for the uplink transmission of beamspace massive multiple-input multiple-output (MIMO) system with low-resolution analog to digital converters (LADCs), to alleviate the performance bottleneck caused by the multi-user interference and quantization noise, with reduced hardware cost and power consumption. To this end, we formulate the optimization of the proposed SHC scheme as a system energy efficiency maximization problem under some practical constraints. The resulting problem contains the highly coupled nonconvex objective function, as well as the discrete binary constraints. By exploiting some fractional programming (FP) techniques and introducing auxiliary variables, we first recast the original challenging problem into a more tractable yet equivalent form. We then develop an efficient double-loop iterative algorithm based on the penalty dual decomposition (PDD) method to find its local stationary solutions. Finally, simulation results verify the effectiveness of the proposed SHC scheme by numerical examples in terms of the achieved system energy efficiency.

This paper considers the uplink of multiuser multiple-input multiple-output systems, where several mobile stations (MSs) cooperatively transmit hybrid messages, including common messages and private messages, to a single base station (BS). We aim to jointly design transmit precoding at the MSs' side and antenna selection at the BS side to maximize the achievable system throughput while reducing implementation complexity. The problem at hand is nonconvex and difficult to solve due to the antenna selection constraint. By exploiting the problem structure and linear relaxation, we propose using the Frank-Wolfe method and the well-known weighted mean-square error minimization approach to tackle the problem, leading to an efficient iterative algorithm. Moreover, due to the large number of antennas, the sparsity of antenna selection is also taken into account by introducing an l0-norm penalty function into the objective function. To tackle this nonconvex and discontinuous problem, we resort to quadratic approximation with smooth optimization and extend our proposed algorithm to the sparse optimization problem. The convergence of the proposed algorithms is analyzed and its effectiveness is verified by numerical examples in terms of the achieved system throughput.

This paper studies the multiple-input multiple- output (MIMO) millimeter wave (mmWave) systems with non-linear power consumption model for 5G network. A new non-linear power consumption model is investigated, consisting of the power cost generated by the circuit and the non-linear power amplifiers. In this work, we aim to optimize the hybrid transceiver to maximize the system capacity subject to the resultant non-linear power constraint. In order to address this problem, we first transform the original optimization problem to a more tractable problem based on the weighted minimum mean squared error (WMMSE) approach. Then, we propose a novel transceiver design algorithm based on the penalty dual decomposition (PDD) optimization framework to address this problem. Moreover, a simplified algorithm is also proposed by using linear approximation. The effectiveness of the proposed algorithm is verified by simulation results.

This paper considers the uplink of large-scale multiple-user multiple-input multiple-output (MU-MIMO) millimeter wave (mmWave) systems, where a number of mobile stations (MSs) communicate with a single base station (BS) equipped with a large-scale antenna array, for application to fifth generation (5G) wireless networks. Within this context, the use of hybrid transceivers along with antenna selection can significantly reduce the implementation cost and energy consumption of analog phase shifters and low-noise amplifiers (LNA). We aim to jointly design the MS beamforming vectors, the hybrid receiving matrices (baseband and analog) and the antenna selection matrix at the BS in order to maximize the achievable system sum-rate. By exploiting the special structure of the problem and linear relaxation, we first convert this problem into three subproblems which are solved via an alternating optimization (AO) method. Specifically, the antenna selection matrix is optimized via the concave-convex procedure (CCCP); the weighted mean-square error minimization (WMMSE) approach is used to find the solution for the transmit beamformer; and the hybrid receiver is obtained via manifold optimization (MO). The convergence of the proposed algorithm is analysed and its effectiveness is verified by simulation.

Millimeter wave (mmWave) systems with large number of antennas are considered as an enabling technology for the fifth generation (5G) cellular networks. For such systems, the traditional fully digital precoding is impractical due to the high cost of radio frequency (RF) chains. To overcome this difficulty, hybrid precoding (HP) is considered. However, in the conventional HP architecture, the number of analog phase shifters (APSs) and RF adders increases linearly with respect to the number of transmit antennas, leading to considerable energy consumption. In this paper, an energy-efficient weighted minimum mean square error (WMMSE) based hybrid precoding algorithm is proposed to maximize the achievable system sum-rate. Through a novel adaptive connection network, a partially-connected HP structure is employed to implement the design of the RF precoder, where each RF chain is connected to only a part of antennas. Given the RF precoder and combiner, we can optimize the baseband precoder and combiner by using WMMSE algorithm. Numerical results show that the proposed algorithm can achieve near optimal sum-rate performance and significantly improve the energy efficiency as compared to the conventional HP algorithm.

This paper considers the uplink of large-scale multiple-user multiple-input multiple-output millimeter wave systems, where several mobile stations (MSs) communicate with a single base station (BS) equipped with a large-scale antenna array, for application to fifth generation wireless networks. Within this context, the use of hybrid transceivers along with antenna selection can significantly reduce the implementation cost and energy consumption of analog phase shifters and low-noise amplifiers. We aim to jointly design the MS beamforming vectors, the hybrid receiving matrices (baseband and analog), and the antenna selection matrix at the BS in order to maximize the achievable system sum-rate under a set of constraints. The corresponding optimization problem is nonconvex and difficult to solve, mainly due to the receive antenna selection and constant modulus constraints on the analog receiving matrix. By exploiting the special structure of the problem and linear relaxation, we first convert this problem into three subproblems, which are solved via an alternating optimization method. The latter iteratively updates the antenna selection matrix, the transmit beamforming vectors, and the hybrid receiving matrices by sequentially addressing each subproblem while keeping the other variables fixed. Specifically, the antenna selection matrix is optimized via the concave-convex procedure; the weighted mean-square error minimization approach is used to find the solution for the transmit beamformer; and the hybrid receiver is obtained via manifold optimization. The convergence of the proposed algorithm is analyzed and its effectiveness is verified by simulation.