Chebyshev-periodical successive over-relaxation was recently proposed as a method of accelerating the convergence speed of fixed-point iterations. If a PSOR iteration is influenced by stochastic disturbances, such as Gaussian noise, then the behavior of the PSOR iteration deviates from the predicted behavior of the noiseless iterations, i.e., the convergence behavior of the Chebyshev-PSOR is highly sensitive to the noises. This paper presents a concise formula for the asymptotic mean squared error (AMSE) of the noisy PSOR iterations. A PSOR iteration can be regarded as a stochastic difference equation and spectral decomposition plays a key role to reveal the asymptotic behaviors of the error covariance. Based on the AMSE formula, a noise mitigation method is developed to reduce the effects of the stochastic disturbance.

Successive interference cancellation (SIC) is a fundamental decoding technique for Gaussian multiple access channels (GMAC). In SIC, transmit signals of each user are separately decoded. In this paper, we analyze an asymptotic decoding threshold of SIC decoding for practical low-density parity-check (LDPC) codes over$N$-user GMAC. Conventionally, the decoding thresholds are evaluated based on the so-called channel approximation (CA) in which the channel model of each decoding stage of a SIC decoder is approximated by simple Gaussian noise channels resulting in errors of decoding thresholds. To avoid this, we propose a refined density evolution (DE) analysis called DE-SIC which uses mixed-Gaussian noise channels corresponding to each decoding stage. We demonstrate DE-SIC by solving a received power optimization problem in GMAC and comparing it to the conventional DE analysis with CA. The results show that DE-SIC accurately evaluates the decoding thresholds whereas the conventional analysis underestimates the thresholds.

A novel linear transform is presented which is suitable for noisy fronthaul channels in distributed MIMO C-RAN systems. A linear transform based on the Karhunen-Loeve transform is optimized in terms of mean squared error (MSE). Using MSE as the objective function enables us to derive a concise closed MSE formula. By using this MSE formula and the Lagrange multiplier method, the optimal linear transform can be derived in a closed form and no optimization processes are required for designing this transform. We also present a dimension expansion method with a Vandermonde matrix as a noise mitigation method. The MSE formula for the Vandermonde dimension expansion indicates an explicit tradeoff relation be-tween spectral efficiency and energy efficiency of the fronthaul channel. Results from numerical experiments and evaluations support our theoretical arguments.

We propose a novel optimization-based decoding algorithm for LDPC-coded massive MIMO channels. The proposed decoding algorithm is based on a proximal gradient method for solving an approximate maximum a posteriori (MAP) decoding problem. The key idea is the use of a code-constraint polynomial penalizing a vector far from a codeword as a regularizer in the approximate MAP objective function. The code proximal operator is naturally derived from code-constraint polynomials. The proposed algorithm, called proximal decoding, can be described by a simple recursion consisting of the gradient descent step for a negative log-likelihood function and the code proximal operation. Several numerical experiments show that the proposed algorithm outperforms known massive MIMO detection algorithms, such as an MMSE detector with belief propagation decoding.

A novel method, termed Chebyshev periodical successive over-relaxation (PSOR), for accelerating the convergence speed of fixed-point iterations is presented. Chebyshev PSOR can be regarded as a variant of successive over-relaxation utilizing the inverse of roots of a Chebyshev polynomial as iteration-dependent PSOR factors. One of the most notable features of the proposed method is that it can be applied to nonlinear fixed-point iterations in addition to linear fixed-point iterations. From several numerical experiments, it is shown that Chebyshev PSOR leads to faster convergence for wide classes of linear and non-linear fixed-point iterations including proximal gradient methods such as ISTA.

Multicast beamforming is a promising technique for multicast communication. Providing an efficient and powerful beamforming design algorithm is a crucial issue because multicast beamforming problems such as a max-min-fair problem are NP-hard in general. Recently, deep learning-based approaches have been proposed for beamforming design. Although these approaches using deep neural networks exhibit reasonable performance gain compared with conventional optimization-based algorithms, their scalability is an emerging problem for large systems in which beamforming design becomes a more demanding task. In this paper, we propose a novel deep unfolded trainable beamforming design with high scalability and efficiency. The algorithm is designed by expanding the recursive structure of an existing algorithm based on projections onto convex sets and embedding a constant number of trainable parameters to the expanded network, which leads to a scalable and stable training process. Numerical results show that the proposed algorithm can accelerate its convergence speed by using unsupervised learning, which is a challenging training process for deep unfolding.

Complex-field signal recovery problems from noisy linear/nonlinear measurements appear in many areas of signal processing and wireless communications. In this paper, we propose a trainable iterative signal recovery algorithm named complex-field TISTA (C-TISTA) which treats complex-field nonlinear inverse problems. C-TISTA is based on the concept of deep unfolding and consists of a gradient descent step with the Wirtinger derivatives followed by a shrinkage step with a trainable complex-valued shrinkage function. Importantly, it contains a small number of trainable parameters so that its training process can be executed efficiently. Numerical results indicate that C-TISTA shows remarkable signal recovery performance compared with existing algorithms.

Compute-and-forward (CAF) relaying is an effective way to increase bandwidth efficiency of wireless two-way relay channels. Design of error-correcting codes and their decoding algorithms suitable for CAF relaying schemes remains an important issue to be studied. In this paper, we will analyze an asymptotic behavior of LDPC codes over two-way relay channels based on density evolution (DE). Because of the asymmetric characteristics of the channel, we use the population dynamics DE combined with DE formulas for asymmetric channels to obtain the belief propagation (BP) thresholds. Additionally, we also evaluate the asymptotic performance of spatially coupled LDPC codes for two-way relay channels. The results indicate that the spatially coupled codes yield improvements in the BP threshold compared with corresponding uncoupled codes for two-way relay channels.

The paper presents a deep learning-aided iterative detection algorithm for massive overloaded MIMO systems. Since the proposed algorithm is based on the projected gradient descent method with trainable parameters, it is named as trainable projected descent-detector (TPG-detector). The trainable internal parameters can be optimized with standard deep learning techniques such as back propagation and stochastic gradient descent algorithms. This approach referred to as data-driven tuning brings notable advantages of the proposed scheme such as fast convergence. The numerical experiments show that TPG-detector achieves comparable detection performance to those of the known algorithms for massive overloaded MIMO channels with lower computation cost.

The compute-and-forward (CAF) scheme has attracted great interests due to its high band-width efficiency on two-way relay channels. In the CAF scheme, a relay attempts to decode a linear combination of transmitted messages from other terminals or relays. It is a crucial issue to study practical error-correcting codes in order to realize the CAF scheme with low computational complexity. In this paper, we present an efficient bit-interleaved coded modulation (BICM) scheme for the CAF scheme with phase shift keying (PSK) modulations. In particular, we examine the asymptotic decoding performance of the BICM scheme with low-density parity-check (LDPC) codes by using the density evolution (DE) method. Based on the asymmetric nature of the channel model, we utilize the population dynamics method for the DE equations without the all-zero codeword assumption. The results show that, for two-way relay channels with QPSK and 8PSK modulations, the LDPC-BICM scheme provides higher achievable rate compared with an alternative separation decoding scheme.

We present a novel optimization-based decoding algorithm for LDPC codes that is suitable for hardware architectures specialized to feed-forward neural networks. The algorithm is based on the projected gradient descent algorithm with a penalty function for solving a non-convex minimization problem. The proposed algorithm has several internal parameters such as step size parameters, a softness parameter, and the penalty coefficients. We use a standard tool set of deep learning, i.e., back propagation and stochastic gradient descent type algorithms, to optimize these parameters. Several numerical experiments show that the proposed algorithm outperforms the belief propagation decoding in some cases.

Connectivity of wireless sensor networks (WSNs) is a fundamental global property expected to be maintained even though some sensor nodes are at fault. In this paper, we investigate the connectivity of random geometric graphs (RGGs) in the node fault model as an abstract model of ad hoc WSNs with unreliable nodes. In the model, each node is assumed to be stochastically at fault, i.e., removed from a graph. As a measure of reliability, the network breakdown probability is then defined as the average probability that a resulting survival graph is disconnected over RGGs. We examine RGGs with general connection functions as an extension of a conventional RGG model and provide two mathematical analyses: the asymptotic analysis for infinite RGGs that reveals the phase transition thresholds of connectivity, and the non-asymptotic analysis for finite RGGs that provides a useful approximation formula. Those analyses are supported by numerical simulations in the Rayleigh SISO model reflecting a practical wireless channel.

A low-precision analog-to-digital converter (ADC) is required to implement a frontend device of wideband digital communication systems in order to reduce its power consumption. The goal of this paper is to present a novel quantizer optimization method for minimizing lower-precision quantizers matched to the sum-product algorithms. The principal idea is to introduce a quantizer that includes a feed-forward neural network and the soft staircase function. Since the soft staircase function is differentiable and has non-zero gradient values everywhere, we can exploit backpropagation and a stochastic gradient descent method to train the feed-forward neural network in the quantizer. The expected loss regarding the channel input and the decoder output is minimized in a supervised training phase. The experimental results indicate that the quantizer optimization method successfully provides an 8-level quantizer for a low-density parity-check (LDPC) code that achieves only a 0.1-dB performance loss compared to the unquantized system.

Compute-and-forward relaying is effective to increase bandwidth efficiency of wireless two-way relay channels. In a compute-and-forward scheme, a relay tries to decode a linear combination composed of transmitted messages from other terminals or relays. Design for error correcting codes and its decoding algorithms suitable for compute-and-forward relaying schemes are still important issue to be studied. In this paper, we will present an asymptotic performance analysis on LDPC codes over two-way relay channels based on density evolution (DE). Because of the asymmetric nature of the channel, we employ the population dynamics DE combined with DE formulas for asymmetric channels to obtain BP thresholds. In addition, we also evaluate the asymptotic performance of spatially coupled LDPC codes for two-way relay channels. The results indicate that the spatial coupling codes yield improvements in the BP threshold compared with corresponding uncoupled codes for two-way relay channels.

k-connectivity of random graphs is a fundamental property indicating reliability of multi-hop wireless sensor networks (WSN). WSNs comprising of sensor nodes with limited power resources are modeled by random graphs with unreliable nodes, which is known as the node fault model. In this paper, we investigate k-connectivity of random graphs in the node fault model by evaluating the network breakdown probability, i.e., the disconnectivity probability of random graphs after stochastic node removals. Using the notion of a strongly typical set, we obtain universal asymptotic upper and lower bounds of the network breakdown probability. The bounds are applicable both to random graphs and to random geometric graphs. We then consider three representative random graph ensembles: the Erdös-Rényi random graph as the simplest case, the random intersection graph for WSNs with random key predistribution schemes, and the random geometric graph as a model of WSNs generated by random sensor node deployment. The bounds unveil the existence of the phase transition of the network breakdown probability for those ensembles.