This paper proposes two full-digital receive beamforming (BF) methods for low-complexity and high-accuracy uplink signal detection via Gaussian belief propagation (GaBP) at base stations (BSs) adopting massive multi-input multi-output (MIMO) for open radio access network (O-RAN). In addition, beyond fifth generation mobile communication (beyond 5G) systems will increase uplink capacity. In the scenarios such as O-RAN and beyond 5G, it is vital to reduce the cost of the BSs by limiting the bandwidth of fronthaul (FH) links, and the dimensionality reduction of the received signal based on the receive BF at a radio unit is a well-known strategy to reduce the amount of data transported via the FH links. In this paper, we clarify appropriate criteria for designing a BF weight considering the subsequent GaBP signal detection with the proposed methods: singular-value-decomposition-based BF and QR-decomposition-based BF with the aid of discrete-Fourier-transformation-based spreading. Both methods achieve the dimensionality reduction without compromising the desired signal power by taking advantage of a null space of channels. The proposed receive BF methods reduce correlations between the received signals in the BF domain, which improves the robustness of GaBP against spatial correlation among fading coefficients. Simulation results assuming realistic BS and user equipment arrangement show that the proposed methods improve detection capability while significantly reducing the computational cost.

The design and adjustment of the divergence in audio applications using nonnegative matrix factorization (NMF) is still open problem. In this study, to deal with this problem, we explore a representation of the divergence using neural networks (NNs). Instead of the divergence, our approach extends the multiplicative update algorithm (MUA), which estimates the NMF parameters, using NNs. The design of the extended MUA incorporates NNs, and the new algorithm is referred to as the deep MUA (DeMUA) for NMF. While the DeMUA represents the algorithm for the NMF, interestingly, the divergence is obtained from the incorporated NN. In addition, we propose theoretical guides to design the incorporated NN such that it can be interpreted as a divergence. By appropriately designing the NN, MUAs based on existing divergences with a single hyper-parameter can be represented by the DeMUA. To train the DeMUA, we applied it to audio denoising and supervised signal separation. Our experimental results show that the proposed architecture can learn the MUA and the divergences in sparse denoising and speech separation tasks and that the MUA based on generalized divergences with multiple parameters shows favorable performances on these tasks.

This paper addresses short-length sparse superposition codes (SSCs) over the additive white Gaussian noise channel. Damped approximate message-passing (AMP) is used to decode short SSCs with zero-mean independent and identically distributed Gaussian dictionaries. To design damping factors in AMP via deep learning, this paper constructs deep-unfolded damped AMP decoding networks. An annealing method for deep learning is proposed for designing nearly optimal damping factors with high probability. In annealing, damping factors are first optimized via deep learning in the low signal-to-noise ratio (SNR) regime. Then, the obtained damping factors are set to the initial values in stochastic gradient descent, which optimizes damping factors for slightly larger SNR. Repeating this annealing process designs damping factors in the high SNR regime. Numerical simulations show that annealing mitigates fluctuation in learned damping factors and outperforms exhaustive search based on an iteration-independent damping factor.

Deep unfolding is a promising deep-learning technique, whose network architecture is based on expanding the recursive structure of existing iterative algorithms. Although deep unfolding realizes convergence acceleration, its theoretical aspects have not been revealed yet. This study details the theoretical analysis of the convergence acceleration in deep-unfolded gradient descent (DUGD) whose trainable parameters are step sizes. We propose a plausible interpretation of the learned step-size parameters in DUGD by introducing the principle of Chebyshev steps derived from Chebyshev polynomials. The use of Chebyshev steps in gradient descent (GD) enables us to bound the spectral radius of a matrix governing the convergence speed of GD, leading to a tight upper bound on the convergence rate. Numerical results show that Chebyshev steps numerically explain the learned step-size parameters in DUGD well.

This paper presents a high-speed SHA-1 implementation. Unlike the conventional unfolding transformation, the proposed unfolding transformation technique makes the combined hash operation blocks to have almost the same delay overhead regardless of the unfolding factor. It can achieve high throughput of SHA-1 implementation by avoiding the performance degradation caused by the first hash computation. We demonstrate the proposed SHA-1 architecture on a FPGA chip. From the experimental results, the SHA-1 architecture with unfolding factor 5 shows 1.17 Gbps. The proposed SHA-1 architecture can achieve about 31% performance improvements compared to its counterparts. Thus, the proposed SHA-1 can be applicable for the security of the high-speed but compact mobile appliances.

This paper presents a multiple-voltage high-level synthesis approach for low power DSP applications using algorithmic transformation techniques. Our approach is motivated by maximization of task mobilities in that the increase of mobilities may raise the possibility of assigning tasks to low-voltage components. The mobility means the ability to schedule the starting time of a task. It is defined as the distance between its as-late-as-possible (ALAP) schedule time and its as-soon-as-possible (ASAP) schedule time. To earn task mobilities, we use loop shrinking, retiming and unfolding techniques. The loop shrinking can first reduce the iteration period bound (IPB) and, then, the others are employed for shortening the iteration period (IP) as much as possible. The minimization of IP results in high task mobilities. Finally, we can assign tasks with high mobilities to low-voltage components and, thus, minimize energy under resource and latency constraints. With considering the overhead of level conversion, our approach can achieve significant power reduction. In the case of the third-order IIR filter, the proposed approach can save up to 40.2% of power consumption.

This paper proposes an algorithm for analyzing the reachability property of Petri nets by the use of unfoldings. It is known that analyzing the reachability by using unfoldings requires exponential time and space to the size of unfolding. The algorithm is based on the branch and bound technique, and experimental results show efficiency of the algorithm.

Unfolding originally introduced by McMillan is gaining ground as a partial-order based method for the verification of concurrent systems without state space explosion. However, it can be exposed to redundancy which may increase its size exponentially. So far, there have been trials to reduce such redundancy resulting from conflicts by improving McMillan's cut-off criterion. In this paper, we show that concurrency is also another cause of redundancy in unfolding, and present an algorithm to reduce such redundancy in live, bounded and reversible Petri nets which is independent of any cut-off algorithm.

Petri nets are widely recognized as a powerful model for discrete event systems. Petri nets have both graphical and mathematical features. Graphical feature provides an environment to design and to comprehend discrete event systems. Mathematical feature provides an analysis power for verifying several properties of such systems. Several analysis techniques have been proposed so far, such as a reachability (coverability) graph method, a matrix equation approach, reduction or decomposition techniques, a symbolic model method and an unfolding method. The unfolding method was introduced to avoid generating the reachability graph. Unfoldings are often used in the verification of asynchronous circuits. This paper focuses on an analysis of finite state systems, i.e., bounded nets, and discuss a reachability problem and a upper bound problem. Relations between these problems and an unfolding have been clarified to provide a novel method to resolve these problems.