Efficient Quantization Scheme Research Articles

Integer‐Sheet‐Pump Quantization for Hexahedral Meshing

AbstractSeveral state‐of‐the‐art algorithms for semi‐structured hexahedral meshing involve a so called quantization step to decide on the integer DoFs of the meshing problem, corresponding to the number of hexahedral elements to embed into certain regions of the domain. Existing reliable methods for quantization are based on solving a sequence of integer quadratic programs (IQP). Solving these in a timely and predictable manner with general‐purpose solvers is a challenge, even more so in the open‐source field. We present here an alternative robust and efficient quantization scheme that is instead based on solving a series of continuous linear programs (LP), for which solver availability and efficiency are not an issue. In our formulation, such LPs are used to determine where inflation or deflation of virtual hexahedral sheets are favorable. We compare our method to two implementations of the former IQP formulation (using a commercial and an open‐source MIP solver, respectively), finding that (a) the solutions found by our method are near‐optimal or optimal in most cases, (b) these solutions are found within a much more predictable time frame, and (c) the state of the art run time is outperformed, in the case of using the open‐source solver by orders of magnitude.

Quadratic variable step-size quantization for efficient raw-data acquisition of image sensors

This paper verifies, via simulations, that quadratic quantization is the most efficient quantization scheme for image-sensor raw-data acquisition. First, discrete-input quadratic quantizers for quantizing the number of photons that sensor pixels receive are developed. Using the discrete-input quadratic quantizers, it is shown that multi-bit QIS outputs can be quantized without loss of image information. Next, artificially generated extremely weak-signal regions are employed to show that quadratic quantizers can preserve all the image information using much lower bit-depth than linear and exponential quantizers. It is concluded that quadratic quantizers should be hardware implemented in image sensors and there is no need to keep linear raw data for the final output of image sensors.

High-Performance VLSI Architecture of DLMS Adaptive Filter for Fast-Convergence and Low-MSE

This brief presents a high-performance VLSI architecture of delayed least mean square (DLMS) adaptive filter for fast-convergence and low-mean square error (MSE) using distributed arithmetic (DA). The proposed design estimates response against the adaptation delays using a parallel predictive adder tree followed by a shift accumulate (SA) unit. An efficient quantization scheme with two bits of scaled error signal is also suggested. Single SA unit for multiple DA bases is used to reduce the number of adders and registers. Simulation and synthesis results show that the proposed design for 32 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order provides 19.72% lesser area, 25.51% lesser power, lesser 28.89% MSE and 59.91% lesser MSE/area over the best existing design.

High-Throughput and Improved-Convergent Design of Pipelined Adaptive DFE for 5G Communication

This brief presents a high-throughput and improved convergent design of pipelined adaptive decision feedback equalizer (ADFE) for 5G communication system. The proposed ADFE design achieves 3.3 Gbps for 4-quadrature amplitude modulation (4-QAM) and 8th order feedback filter (FBF). A novel look-up table update scheme for M-ary QAM ADFE is proposed. Further, we present an efficient quantization scheme for the proposed design. Theoretical derivations and simulation results confirm that the convergence performance of the proposed ADFE is superior. For instance, the proposed design for 16-QAM and 16th order FBF takes 167 less iterations and improves 4.03 dB error performance, while it provides nearly 8.96 times higher throughput as compared to the best existing design.

An Efficient Deep Learning Framework for Low Rate Massive MIMO CSI Reporting

Channel state information (CSI) reporting is important for multiple-input multiple-output (MIMO) wireless transceivers to achieve high capacity and energy efficiency in frequency division duplex (FDD) mode. CSI reporting for massive MIMO systems could consume large bandwidth and degrade spectrum efficiency. Deep learning (DL)-based CSI reporting integrated with channel characteristics has demonstrated success in improving CSI compression and recovery. To further improve the encoding efficiency of CSI feedback, we develop an efficient DL-based compression framework CQNet to jointly tackle CSI compression, codeword quantization, and recovery under the bandwidth constraint. CQNet is directly compatible with other DL-based CSI feedback works for further enhancement. We propose a more efficient quantization scheme in the radial coordinate by introducing a novel magnitude-adaptive phase quantization framework. Compared with traditional CSI reporting, CQNet demonstrates superior CSI feedback efficiency and better CSI reconstruction accuracy.

Space Efficient Quantization for Deep Convolutional Neural Networks

Deep convolutional neural networks (DCNNs) have shown outstanding performance in the fields of computer vision, natural language processing, and complex system analysis. With the improvement of performance with deeper layers, DCNNs incur higher computational complexity and larger storage requirement, making it extremely difficult to deploy DCNNs on resource-limited embedded systems (such as mobile devices or Internet of Things devices). Network quantization efficiently reduces storage space required by DCNNs. However, the performance of DCNNs often drops rapidly as the quantization bit reduces. In this article, we propose a space efficient quantization scheme which uses eight or less bits to represent the original 32-bit weights. We adopt singular value decomposition (SVD) method to decrease the parameter size of fully-connected layers for further compression. Additionally, we propose a weight clipping method based on dynamic boundary to improve the performance when using lower precision. Experimental results demonstrate that our approach can achieve up to approximately 14x compression while preserving almost the same accuracy compared with the full-precision models. The proposed weight clipping method can also significantly improve the performance of DCNNs when lower precision is required.

Accelerating Recurrent Neural Networks: A Memory-Efficient Approach

Recurrent neural networks (RNNs) have achieved the state-of-the-art performance on various sequence learning tasks due to their powerful sequence modeling capability. However, RNNs usually require a large number of parameters and high computational complexity. Hence, it is quite challenging to implement complex RNNs on embedded devices with stringent memory and latency requirement. In this paper, we first present a novel hybrid compression method for a widely used RNN variant, long-short term memory (LSTM), to tackle these implementation challenges. By properly using circulant matrices, forward nonlinear function approximation, and efficient quantization schemes with a retrain-based training strategy, the proposed compression method can reduce more than 95% of memory usage with negligible accuracy loss when verified under language modeling and speech recognition tasks. An efficient scalable parallel hardware architecture is then proposed for the compressed LSTM. With an innovative chessboard division method for matrix-vector multiplications, the parallelism of the proposed hardware architecture can be freely chosen under certain latency requirement. Specifically, for the circulant matrix-vector multiplications employed in the compressed LSTM, the circulant matrices are judiciously reorganized to fit in with the chessboard division and minimize the number of memory accesses required for the matrix multiplications. The proposed architecture is modeled using register transfer language (RTL) and synthesized under the TSMC 90-nm CMOS technology. With 518.5-kB on-chip memory, we are able to process a 512×512 compressed LSTM in 1.71 μs, corresponding to 2.46 TOPS on the uncompressed one, at a cost of 30.77-mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> chip area. The implementation results demonstrate that the proposed design can achieve significantly high flexibility and area efficiency, which satisfies many real-time applications on embedded devices. It is worth mentioning that the memory-efficient approach of accelerating LSTM developed in this paper is also applicable to other RNN variants.

Controlled synchronization of discrete-time nonlinear systems under constrained communication

Consideration was given to the problem of synchronizing the master and slave nonlinear discrete systems interrelated through a communication-constrained channel. The effect of quantization error was examined, and an efficient quantization scheme was proposed such that the error of transmission vanishes under constrained communications. The desired data transmission rate was calculated. A control law such that the error of quantized synchronization is input-to-state stable with respect to the transmission error was constructed in terms of the linear matrix inequalities. The proposed scheme supports full quantized synchronization of the master and slave systems. The result obtained was exemplified by a model of simply connected flexible joint robot.

Scheduling in OFDMA Uplink With Imperfect CSI

Uplink scheduling in OFDMA systems with imperfect CSI is investigated. An efficient CSI quantization scheme is proposed and shown to achieve good perfor- mance with a limited number of quantization bits in the perfect CSI scenario. The probability of error in quantizing imperfect CSI is studied and analytical formulas are derived. Simulation results are presented and show that the errors in estimating the CSI are to a large extent absorbed by the quantization error and the performance with quan- tized imperfect CSI is close to full CSI even with a reduced number of quantization bits.

A Modified Run-Length Coding towards the Realization of a RRO-NRDPWT-Based ECG Data Compression System

The wavelet-based approach that combines a reversible round-off nonrecursive discrete periodized wavelet transform (RRO-NRDPWT) and the set partitioning in hierarchical trees (SPIHT) scheme is an efficient ECG data compression. However, this RRO-NRDPWT-based system suffers from the high complexity of the SPIHT scheme during realization. In this paper, a modified run-length coding (MRLC) algorithm is proposed towards the realization of a RRO-NRDPWT-based ECG data compression system. The MRLC with its regularity and low computational complexity is suitable for hardware implementation, but at a cost of compression performance. This sacrifice is compensated by an efficient quantization scheme. By using the MIT-BIH arrhythmia database, the experimental results show that the proposed scheme can compete with the SPIHT scheme for a compression ratio (CR) greater than 8. Hardware simulations are taken using both the Verilog logic simulator with Cadence design platform, and a Xilinx FPGA EP2C35F672C6.

Sensor Allocation and Quantization Schemes for Multi-Band Cognitive Radio Cooperative Sensing System

We investigate cooperative sensing schemes for a cognitive radio (CR) network operating in multiple primary bands. The CR spectrum sensors use energy detection to identify the presence of the primary signals. We consider a parallel fusion architecture in which all the sensing devices send their binary quantized sensing information to an access point, which then applies a fusion rule to determine the presence of a primary user in each band. In this paper, we first propose schemes to assign sensors to various primary bands. We then study efficient quantization schemes when `OR' fusion rule is used in each band at the access point. We show that the optimal quantization scheme is, in general, non-convex and propose a suboptimal solution based on convex restriction of the original problem. We further study quantization schemes for general k-out-of-N fusion rule. We compare the performance of the proposed schemes using simulations.

A Modified Run-Length Coding for the Realization of Wavelet-based ECG Data Compression System

With high compression performance, realization of wavelet-based data compression system is crucial for multi-lead ECG signal recording. In this paper, a modified run-length coding (MRLC) algorithm associated with an efficient quantization scheme is proposed for the realization of a RRO-NRDPWT-based ECG data compression system. The MRLC with regularity and low computational complexity is suitable for hardware implementation at a cost of compression performance. This sacrifice will be compensated by the new quantization scheme. By using the MIT-BIH arrhythmia database, the experimental results show that the proposed scheme can be competitive to other wavelet-based approaches in compression performance. In addition, the MRLC can improve traditional run-length coding by about 13%.

Split Table Extension: A Low Complexity LVQ Extension Scheme in Low Bitrate Audio Coding

Embedded algebraic vector quantization (EAVQ) is a fast and efficient lattice vector quantization (LVQ) scheme used in low-bitrate audio coding. However, a defect of EAVQ is the overload distortion which causes unpleasant noises in audio coding. To solve this problem, specific base codebook extension schemes should be carefully considered. In this letter, we present a novel EAVQ codebook extension scheme-split table extension (STE), which splits a vector into two smaller vectors: one in the base codebook and the other in the split table. The base codebook and the split table are designed according to the appearance probability of quantized vectors in audio segments. Experiments on encoding multiple audio and speech sequences show that, compared with the existed Voronoi extension scheme, STE greatly reduces computation complexity and storage requirement while achieving similar coding quality.

Efficient variable rate vector quantization using quadtree segmentation

In video and image compression, vector quantization can be fixed rate or variable rate depending on how the encoding codebook is structured. Previous variable rate vector quantization schemes using greedy tree growing algorithm partitions images into fixed size blocks and has not exploited the correlation in the low detail blocks. A new and efficient variable rate vector quantization scheme based on variable block size quadtree segmentation is proposed in this paper. Simulation results show that the proposed variable block size variable rate vector quantization scheme achieved better subjective image quality with higher PSNR at a reduced bit rate as compared with the fixed block size variable rate vector quantization scheme.

Source coding of the discrete Fourier transform

Distortion-rate theory is used to derive absolute performance bounds and encoding guidelines for direct fixed-rate minimum mean-square error data compression of the discrete Fourier transform (DFT) of a stationary real or circularly complex sequence. Both real-part-imaginary-part and magnitude-phase-angle encoding are treated. General source coding theorems are proved in order to justify using the optimal test channel transition probability distribution for allocating the information rate among the DFT coefficients and for calculating arbitrary performance measures on actual optimal codes. This technique has yielded a theoretical measure of the relative importance of phase angle over the magnitude in magnitude-phase-angle data compression. The result is that the phase angle must be encoded with 0.954 nats, or 1.37 bits, more rate than the magnitude for rates exceeding 3.0 nats per complex element. This result and the optimal error bounds are compared to empirical results for efficient quantization schemes.