In this letter, a novel projection algorithm is proposed in which projection onto a triangle consisting of the three even-vertices closest to the vector to be projected replaces check polytope projection, achieving the same FER performance as exact projection algorithm in both high-iteration and low-iteration regime. Simulation results show that compared with the sparse affine projection algorithm (SAPA), it can improve the FER performance by 0.2 dB as well as save average number of iterations by 4.3%.

The Euclidean projection operation is the most complex and time-consuming of the alternating direction method of multipliers (ADMM) decoding algorithms, resulting in a large number of resources when deployed on hardware platforms. We propose a simplified line segment projection algorithm (SLSA) and present the hardware design and the quantization scheme of the SLSA. In simulation results, the proposed SLSA module has a better performance than the original algorithm with the same fixed bitwidths due to the centrosymmetric structure of SLSA. Furthermore, the proposed SLSA module with a simpler structure without hypercube projection can reduce time consuming by up to 72.2% and reduce hardware resource usage by more than 87% compared to other Euclidean projection modules in the experiments.

Linear programming (LP) decoding based on the alternating direction method of multipliers (ADMM) has proved to be effective for low-density parity-check (LDPC) codes. However, for high-density parity-check (HDPC) codes, the ADMM-LP decoder encounters two problems, namely a high-density check matrix in HDPC codes and a great number of pseudocodewords in HDPC codes' fundamental polytope. The former problem makes the check polytope projection extremely complex, and the latter one leads to poor frame error rates (FER) performance. To address these issues, we introduce the even vertex algorithm (EVA) into the ADMM-LP decoding algorithm for HDPC codes, named as HDPC-EVA. HDPC-EVA can reduce the complexity of the projection process and improve the FER performance. We further enhance the proposed decoder by the automorphism groups of codes, creating diversity in the parity-check matrix. The simulation results show that the proposed decoder is capable of cutting down the average decoding time for each iteration by 30%-60%, as well as achieving near maximum likelihood (ML) performance on some BCH codes.

The combination of large-scale antenna arrays and simultaneous wireless information and power transfer (SWIPT), which can provide enormous increase of throughput and energy efficiency is a promising key in next generation wireless system (5G). This paper investigates efficient transceiver design to minimize transmit power, subject to users' required data rates and energy harvesting, in large-scale SWIPT system where the base station utilizes a very large number of antennas for transmitting both data and energy to multiple users equipped with time-switching (TS) or power-splitting (PS) receive structures. We first propose the well-known semidefinite relaxation (SDR) and Gaussian randomization techniques to solve the minimum transmit power problems. However, for these large-scale SWIPT problems, the proposed scheme, which is based on conventional SDR method, is not suitable due to its excessive computation costs, and a consensus alternating direction method of multipliers (ADMM) cannot be directly applied to the case that TS or PS ratios are involved in the optimization problem. Therefore, in the second solution, our first step is to optimize the variables of TS or PS ratios, and to achieve simplified problems. After then, we propose fast algorithms for solving these problems, where the outer loop of sequential parametric convex approximation (SPCA) is combined with the inner loop of ADMM. Numerical simulations show the fast convergence and superiority of the proposed solutions.

Solving image recovery problems requires the use of some efficient regularizations based on a priori information with respect to the unknown original image. Naturally, we can assume that an image is modeled as the sum of smooth, edge, and texture components. To obtain a high quality recovered image, appropriate regularizations for each individual component are required. In this paper, we propose a novel image recovery technique which performs decomposition and recovery simultaneously. We formulate image recovery as a nonsmooth convex optimization problem and design an iterative scheme based on the alternating direction method of multipliers (ADMM) for approximating its global minimizer efficiently. Experimental results reveal that the proposed image recovery technique outperforms a state-of-the-art method.