Improving LDPC Decoding Performance for 3D TLC NAND Flash by LLR Optimization Scheme for Hard and Soft Decision

Low-density parity-check (LDPC) codes have been widely adopted in NAND flash in recent years to enhance data reliability. There are two types of decoding, hard-decision and soft-decision decoding. However, for the two types, their error correction capability degrades due to inaccurate log-likelihood ratio (LLR) . To improve the LLR accuracy of LDPC decoding, this article proposes LLR optimization schemes, which can be utilized for both hard-decision and soft-decision decoding. First, we build a threshold voltage distribution model for 3D floating gate (FG) triple level cell (TLC) NAND flash. Then, by exploiting the model, we introduce a scheme to quantize LLR during hard-decision and soft-decision decoding. And by amplifying a portion of small LLRs, which is essential in the layer min-sum decoder, more precise LLR can be obtained. For hard-decision decoding, the proposed new modes can significantly improve the decoder’s error correction capability compared with traditional solutions. Soft-decision decoding starts when hard-decision decoding fails. For this part, we study the influence of the reference voltage arrangement of LLR calculation and apply the quantization scheme. The simulation shows that the proposed approach can reduce frame error rate (FER) for several orders of magnitude.

BISWSRBS: A Winograd-based CNN Accelerator with a Fine-grained Regular Sparsity Pattern and Mixed Precision Quantization

Field-programmable Gate Array (FPGA) is a high-performance computing platform for Convolution Neural Networks (CNNs) inference. Winograd algorithm, weight pruning, and quantization are widely adopted to reduce the storage and arithmetic overhead of CNNs on FPGAs. Recent studies strive to prune the weights in the Winograd domain, however, resulting in irregular sparse patterns and leading to low parallelism and reduced utilization of resources. Besides, there are few works to discuss a suitable quantization scheme for Winograd. In this article, we propose a regular sparse pruning pattern in the Winograd-based CNN, namely, Sub-row-balanced Sparsity (SRBS) pattern, to overcome the challenge of the irregular sparse pattern. Then, we develop a two-step hardware co-optimization approach to improve the model accuracy using the SRBS pattern. Based on the pruned model, we implement a mixed precision quantization to further reduce the computational complexity of bit operations. Finally, we design an FPGA accelerator that takes both the advantage of the SRBS pattern to eliminate low-parallelism computation and the irregular memory accesses, as well as the mixed precision quantization to get a layer-wise bit width. Experimental results on VGG16/VGG-nagadomi with CIFAR-10 and ResNet-18/34/50 with ImageNet show up to 11.8×/8.67× and 8.17×/8.31×/10.6× speedup, 12.74×/9.19× and 8.75×/8.81×/11.1× energy efficiency improvement, respectively, compared with the state-of-the-art dense Winograd accelerator [20] with negligible loss of model accuracy. We also show that our design has 4.11× speedup compared with the state-of-the-art sparse Winograd accelerator [19] on VGG16.

Integer-Only CNNs with 4 Bit Weights and Bit-Shift Quantization Scales at Full-Precision Accuracy

Quantization of neural networks has been one of the most popular techniques to compress models for embedded (IoT) hardware platforms with highly constrained latency, storage, memory-bandwidth, and energy specifications. Limiting the number of bits per weight and activation has been the main focus in the literature. To avoid major degradation of accuracy, common quantization methods introduce additional scale factors to adapt the quantized values to the diverse data ranges, present in full-precision (floating-point) neural networks. These scales are usually kept in high precision, requiring the target compute engine to support a few high-precision multiplications, which is not desirable due to the larger hardware cost. Little effort has yet been invested in trying to avoid high-precision multipliers altogether, especially in combination with 4 bit weights. This work proposes a new quantization scheme, based on power-of-two quantization scales, that works on-par compared to uniform per-channel quantization with full-precision 32 bit quantization scales when using only 4 bit weights. This is done through the addition of a low-precision lookup-table that translates stored 4 bit weights into nonuniformly distributed 8 bit weights for internal computation. All our quantized ImageNet CNNs achieved or even exceeded the Top-1 accuracy of their full-precision counterparts, with ResNet18 exceeding its full-precision model by 0.35%. Our MobileNetV2 model achieved state-of-the-art performance with only a slight drop in accuracy of 0.51%.

Quantum groups and polymer quantum mechanics

In Polymer Quantum Mechanics, a quantization scheme that naturally emerges from Loop Quantum Gravity, position and momentum operators cannot be both well defined on the Hilbert space [Formula: see text]. It is henceforth deemed impossible to define standard creation and annihilation operators. In this paper, we show that a [Formula: see text]-oscillator structure, and hence [Formula: see text]-deformed creation/annihilation operators, can be naturally defined on [Formula: see text], which is then mapped into the sum of many copies of the [Formula: see text]-oscillator Hilbert space. This shows that the [Formula: see text]-calculus is a natural calculus for Polymer Quantum Mechanics. Moreover, we show that the inequivalence of different superselected sectors of [Formula: see text] is of topological nature.

Fixed Point Analysis Workflow for efficient Design of Convolutional Neural Networks in Hearing Aids

Neural networks (NN) are a powerful tool to tackle complex problems in hearing aid research, but their use on hearing aid hardware is currently limited by memory and processing power. To enable the training with these constrains, a fixed point analysis and a memory friendly power of two quantization (replacing multiplications with shift operations) scheme has been implemented extending TensorFlow, a standard framework for training neural networks, and the Qkeras package [1, 2]. The implemented fixed point analysis detects quantization issues like overflows, underflows, precision problems and zero gradients. The analysis is done for each layer in every epoch for weights, biases and activations respectively. With this information the quantization can be optimized, e.g. by modifying the bit width, number of integer bits or the quantization scheme to a power of two quantization. To demonstrate the applicability of this method a case study has been conducted. Therefore a CNN has been trained to predict the Ideal Ratio Mask (IRM) for noise reduction in audio signals. The dataset consists of speech samples from the TIMIT dataset mixed with noise from the Urban Sound 8kand VAD-dataset at 0 dB SNR. The CNN was trained in floating point, fixed point and a power of two quantization. The CNN architecture consists of six convolutional layers followed by three dense layers. From initially 1.9 MB memory footprint for 468k float32 weights, the power of two quantized network is reduced to 236 kB, while the Short Term Objective Intelligibility (STOI) Improvement drops only from 0.074 to 0.067. Despite the quantization only a minimal drop in performance was observed, while saving up to 87.5 % of memory, thus being suited for employment in a hearing aid

Two-level systems coupled to Graphene plasmons: A Lindblad equation approach

In this paper, we review the theory of open quantum systems and macroscopic quantum electrodynamics, providing a self-contained account of many aspects of these two theories. The former is presented in the context of a qubit coupled to a electromagnetic thermal bath, the latter is presented in the context of a quantization scheme for surface-plasmon polaritons (SPPs) in graphene based on Langevin noise currents. This includes a calculation of the dyadic Green’s function (in the electrostatic limit) for a Graphene sheet between two semi-infinite linear dielectric media, and its subsequent application to the construction of SPP creation and annihilation operators. We then bring the two fields together and discuss the entanglement of two qubits in the vicinity of a graphene sheet which supports SPPs. The two qubits communicate with each other via the emission and absorption of SPPs. We find that a Schrödinger cat state involving the two qubits can be partially protected from decoherence by taking advantage of the dissipative dynamics in graphene. A comparison is also drawn between the dynamics at zero temperature, obtained via Schrödinger’s equation, and at finite temperature, obtained using the Lindblad equation.

Efficient Channel Feedback Scheme for Multi-User MIMO Hybrid Beamforming Systems

This paper proposes an efficient channel information feedback scheme to reduce the feedback overhead of multi-user multiple-input multiple-output (MU-MIMO) hybrid beamforming systems. As massive machine type communication (mMTC) was considered in the deployments of 5G, a transmitter of the hybrid beamforming system should communicate with multiple devices at the same time. To communicate with multiple devices in the same time and frequency slot, high-dimensional channel information should be used to control interferences between the receivers. Therefore, the feedback overhead for the channels of the devices is impractically high. To reduce the overhead, this paper uses common sparsity of channel and nonlinear quantization. To find a common sparse part of a wide frequency band, the proposed system uses minimum mean squared error orthogonal matching pursuit (MMSE-OMP). After the search of the common sparse basis, sparse vectors of subcarriers are searched by using the basis. The sparse vectors are quantized by a nonlinear codebook that is generated by conditional random vector quantization (RVQ). For the conditional RVQ, the Linde–Buzo–Gray (LBG) algorithm is used in conditional vector space. Typically, elements of sparse vectors are sorted according to magnitude by the OMP algorithm. The proposed quantization scheme considers the property for the conditional RVQ. For feedback, indices of the common sparse basis and the quantized sparse vectors are delivered and the channel is recovered at a transmitter for precoding of MU-MIMO. The simulation results show that the proposed scheme achieves lower MMSE for the recovered channel than that of the linear quantization scheme. Furthermore, the transmitter can adopt analog and digital precoding matrix freely by the recovered channel and achieve higher sum rate than that of conventional codebook-based MU-MIMO precoding schemes.

Loop Quantum Black Hole Extensions Within the Improved Dynamics

We continue our investigation of an improved quantization scheme for spherically symmetric loop quantum gravity. We find that in the region where the black hole singularity appears in the classical theory, the quantum theory contains semi-classical states that approximate general relativity coupled to an effective anisotropic fluid. The singularity is eliminated and the space-time can be continued into a white hole space-time. This is similar to previously considered scenarios based on a loop quantum gravity quantization.

A new approach to anomalous axial vector field theory

In an earlier paper, it has been shown that the ultra violet divergence structure of anomalous [Formula: see text] axial vector gauge model in the stochastic quantization scheme is different from that in the conventional quantum field theory. Also, it has been shown that the model is expected to be renormalizable. Based on the operator formalism of the stochastic quantization, a new approach to anomalous [Formula: see text] axial vector gauge model is proposed. The operator formalism provides a convenient framework for analysis of ultra violet divergences, but the computations in a realistic model become complicated. In this paper a new approach to do computations in the model is formulated directly in four dimensions. The suggestions put forward here will lead to simplification in the study of applications of the axial vector gauge theory, as well as those of other similar models.

Symplectic Quantization I: Dynamics of Quantum Fluctuations in a Relativistic Field Theory

We propose here a new symplectic quantization scheme, where quantum fluctuations of a scalar field theory stem from two main assumptions: relativistic invariance and equiprobability of the field configurations with identical value of the action. In this approach the fictitious time of stochastic quantization becomes a genuine additional time variable, with respect to the coordinate time of relativity. This intrinsic time is associated to a symplectic evolution in the action space, which allows one to investigate not only asymptotic, i.e. equilibrium, properties of the theory, but also its non-equilibrium transient evolution. In this paper, which is the first one in a series of two, we introduce a formalism which will be applied to general relativity in its companion work (Gradenigo, Symplectic quantization II: dynamics of space-time quantum fluctuations and the cosmological constant, 2021).