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  • Nonvolatile Storage Cells Using FiCC for IoT Processors with Intermittent Operations

    Yuki ABE  Kazutoshi KOBAYASHI  Jun SHIOMI  Hiroyuki OCHI  

     
    PAPER

      Pubricized:
    2023/04/13
      Vol:
    E106-C No:10
      Page(s):
    546-555

    Energy harvesting has been widely investigated as a potential solution to supply power for Internet of Things (IoT) devices. Computing devices must operate intermittently rather than continuously, because harvested energy is unstable and some of IoT applications can be periodic. Therefore, processors for IoT devices with intermittent operation must feature a hibernation mode with zero-standby-power in addition to energy-efficient normal mode. In this paper, we describe the layout design and measurement results of a nonvolatile standard cell memory (NV-SCM) and nonvolatile flip-flops (NV-FF) with a nonvolatile memory using Fishbone-in-Cage Capacitor (FiCC) suitable for IoT processors with intermittent operations. They can be fabricated in any conventional CMOS process without any additional mask. NV-SCM and NV-FF are fabricated in a 180nm CMOS process technology. The area overhead by nonvolatility of a bit cell are 74% in NV-SCM and 29% in NV-FF, respectively. We confirmed full functionality of the NV-SCM and NV-FF. The nonvolatile system using proposed NV-SCM and NV-FF can reduce the energy consumption by 24.3% compared to the volatile system when hibernation/normal operation time ratio is 500 as shown in the simulation.

  • Non-Stop Microprocessor for Fault-Tolerant Real-Time Systems Open Access

    Shota NAKABEPPU  Nobuyuki YAMASAKI  

     
    PAPER

      Pubricized:
    2023/01/25
      Vol:
    E106-C No:7
      Page(s):
    365-381

    It is very important to design an embedded real-time system as a fault-tolerant system to ensure dependability. In particular, when a power failure occurs, restart processing after power restoration is required in a real-time system using a conventional processor. Even if power is restored quickly, the restart process takes a long time and causes deadline misses. In order to design a fault-tolerant real-time system, it is necessary to have a processor that can resume operation in a short time immediately after power is restored, even if a power failure occurs at any time. Since current embedded real-time systems are required to execute many tasks, high schedulability for high throughput is also important. This paper proposes a non-stop microprocessor architecture to achieve a fault-tolerant real-time system. The non-stop microprocessor is designed so as to resume normal operation even if a power failure occurs at any time, to achieve little performance degradation for high schedulability even if checkpoint creations and restorations are performed many times, to control flexibly non-volatile devices through software configuration, and to ensure data consistency no matter when a checkpoint restoration is performed. The evaluation shows that the non-stop microprocessor can restore a checkpoint within 5µsec and almost hide the overhead of checkpoint creations. The non-stop microprocessor with such capabilities will be an essential component of a fault-tolerant real-time system with high schedulability.

  • Metadata-Based Quality-Estimation Model for Tile-Based Omnidirectional Video Streaming Open Access

    Yuichiro URATA  Masanori KOIKE  Kazuhisa YAMAGISHI  Noritsugu EGI  

     
    PAPER-Multimedia Systems for Communications

      Pubricized:
    2022/11/15
      Vol:
    E106-B No:5
      Page(s):
    478-488

    In this paper, a metadata-based quality-estimation model is proposed for tile-based omnidirectional video streaming services, aiming to realize quality monitoring during service provision. In the tile-based omnidirectional video (ODV) streaming services, the ODV is divided into tiles, and the high-quality tiles and the low-quality tiles are distributed in accordance with the user's viewing direction. When the user changes the viewing direction, the user temporarily watches video with the low-quality tiles. In addition, the longer the time (delay time) until the high-quality tile for the new viewing direction is downloaded, the longer the viewing time of video with the low-quality tile, and thus the delay time affects quality. From the above, the video quality of the low-quality tiles and the delay time significantly impact quality, and these factors need to be considered in the quality-estimation model. We develop quality-estimation models by extending the conventional quality-estimation models for 2D adaptive streaming. We also show that the quality-estimation model using the bitrate, resolution, and frame rate of high- and low-quality tiles and that the delay time has sufficient estimation accuracy based on the results of subjective quality evaluation experiments.

  • Lookahead Search-Based Low-Complexity Multi-Type Tree Pruning Method for Versatile Video Coding (VVC) Intra Coding

    Qi TENG  Guowei TENG  Xiang LI  Ran MA  Ping AN  Zhenglong YANG  

     
    PAPER-Coding Theory

      Pubricized:
    2022/08/24
      Vol:
    E106-A No:3
      Page(s):
    606-615

    The latest versatile video coding (VVC) introduces some novel techniques such as quadtree with nested multi-type tree (QTMT), multiple transform selection (MTS) and multiple reference line (MRL). These tools improve compression efficiency compared with the previous standard H.265/HEVC, but they suffer from very high computational complexity. One of the most time-consuming parts of VVC intra coding is the coding tree unit (CTU) structure decision. In this paper, we propose a low-complexity multi-type tree (MT) pruning method for VVC intra coding. This method consists of lookahead search and MT pruning. The lookahead search process is performed to derive the approximate rate-distortion (RD) cost of each MT node at depth 2 or 3. Subsequently, the improbable MT nodes are pruned by different strategies under different cost errors. These strategies are designed according to the priority of the node. Experimental results show that the overall proposed algorithm can achieve 47.15% time saving with only 0.93% Bjøntegaard delta bit rate (BDBR) increase over natural scene sequences, and 45.39% time saving with 1.55% BDBR increase over screen content sequences, compared with the VVC reference software VTM 10.0. Such results demonstrate that our method achieves a good trade-off between computational complexity and compression quality compared to recent methods.

  • Modal Interval Regression Based on Spline Quantile Regression

    Sai YAO  Daichi KITAHARA  Hiroki KURODA  Akira HIRABAYASHI  

     
    PAPER-Numerical Analysis and Optimization

      Pubricized:
    2022/07/26
      Vol:
    E106-A No:2
      Page(s):
    106-123

    The mean, median, and mode are usually calculated from univariate observations as the most basic representative values of a random variable. To measure the spread of the distribution, the standard deviation, interquartile range, and modal interval are also calculated. When we analyze continuous relations between a pair of random variables from bivariate observations, regression analysis is often used. By minimizing appropriate costs evaluating regression errors, we estimate the conditional mean, median, and mode. The conditional standard deviation can be estimated if the bivariate observations are obtained from a Gaussian process. Moreover, the conditional interquartile range can be calculated for various distributions by the quantile regression that estimates any conditional quantile (percentile). Meanwhile, the study of the modal interval regression is relatively new, and spline regression models, known as flexible models having the optimality on the smoothness for bivariate data, are not yet used. In this paper, we propose a modal interval regression method based on spline quantile regression. The proposed method consists of two steps. In the first step, we divide the bivariate observations into bins for one random variable, then detect the modal interval for the other random variable as the lower and upper quantiles in each bin. In the second step, we estimate the conditional modal interval by constructing both lower and upper quantile curves as spline functions. By using the spline quantile regression, the proposed method is widely applicable to various distributions and formulated as a convex optimization problem on the coefficient vectors of the lower and upper spline functions. Extensive experiments, including settings of the bin width, the smoothing parameter and weights in the cost function, show the effectiveness of the proposed modal interval regression in terms of accuracy and visual shape for synthetic data generated from various distributions. Experiments for real-world meteorological data also demonstrate a good performance of the proposed method.

  • GRAPHULY: GRAPH U-Nets-Based Multi-Level Graph LaYout

    Kai YAN  Tiejun ZHAO  Muyun YANG  

     
    LETTER-Computer Graphics

      Pubricized:
    2022/09/16
      Vol:
    E105-D No:12
      Page(s):
    2135-2138

    Graph layout is a critical component in graph visualization. This paper proposes GRAPHULY, a graph u-nets-based neural network, for end-to-end graph layout generation. GRAPHULY learns the multi-level graph layout process and can generate graph layouts without iterative calculation. We also propose to use Laplacian positional encoding and a multi-level loss fusion strategy to improve the layout learning. We evaluate the model with a random dataset and a graph drawing dataset and showcase the effectiveness and efficiency of GRAPHULY in graph visualization.

  • Holmes: A Hardware-Oriented Optimizer Using Logarithms

    Yoshiharu YAMAGISHI  Tatsuya KANEKO  Megumi AKAI-KASAYA  Tetsuya ASAI  

     
    PAPER

      Pubricized:
    2022/05/11
      Vol:
    E105-D No:12
      Page(s):
    2040-2047

    Edge computing, which has been gaining attention in recent years, has many advantages, such as reducing the load on the cloud, not being affected by the communication environment, and providing excellent security. Therefore, many researchers have attempted to implement neural networks, which are representative of machine learning in edge computing. Neural networks can be divided into inference and learning parts; however, there has been little research on implementing the learning component in edge computing in contrast to the inference part. This is because learning requires more memory and computation than inference, easily exceeding the limit of resources available for edge computing. To overcome this problem, this research focuses on the optimizer, which is the heart of learning. In this paper, we introduce our new optimizer, hardware-oriented logarithmic momentum estimation (Holmes), which incorporates new perspectives not found in existing optimizers in terms of characteristics and strengths of hardware. The performance of Holmes was evaluated by comparing it with other optimizers with respect to learning progress and convergence speed. Important aspects of hardware implementation, such as memory and operation requirements are also discussed. The results show that Holmes is a good match for edge computing with relatively low resource requirements and fast learning convergence. Holmes will help create an era in which advanced machine learning can be realized on edge computing.

  • Process Variation Based Electrical Model of STT-Assisted VCMA-MTJ and Its Application in NV-FA

    Dongyue JIN  Luming CAO  You WANG  Xiaoxue JIA  Yongan PAN  Yuxin ZHOU  Xin LEI  Yuanyuan LIU  Yingqi YANG  Wanrong ZHANG  

     
    PAPER-Semiconductor Materials and Devices

      Pubricized:
    2022/04/18
      Vol:
    E105-C No:11
      Page(s):
    704-711

    Fast switching speed, low power consumption, and good stability are some of the important properties of spin transfer torque assisted voltage controlled magnetic anisotropy magnetic tunnel junction (STT-assisted VCMA-MTJ) which makes the non-volatile full adder (NV-FA) based on it attractive for Internet of Things. However, the effects of process variations on the performances of STT-assisted VCMA-MTJ and NV-FA will be more and more obvious with the downscaling of STT-assisted VCMA-MTJ and the improvement of chip integration. In this paper, a more accurate electrical model of STT-assisted VCMA-MTJ is established on the basis of the magnetization dynamics and the process variations in film growth process and etching process. In particular, the write voltage is reduced to 0.7 V as the film thickness is reduced to 0.9 nm. The effects of free layer thickness variation (γtf) and oxide layer thickness variation (γtox) on the state switching as well as the effect of tunnel magnetoresistance ratio variation (β) on the sensing margin (SM) are studied in detail. Considering that the above process variations follow Gaussian distribution, Monte Carlo simulation is used to study the effects of the process variations on the writing and output operations of NV-FA. The result shows that the state of STT-assisted VCMA-MTJ can be switched under -0.3%≤γtf≤6% or -23%≤γtox≤0.2%. SM is reduced by 16.0% with β increases from 0 to 30%. The error rates of writing ‘0’ in the NV-FA can be reduced by increasing Vb1 or increasing positive Vb2. The error rates of writing ‘1’ can be reduced by increasing Vb1 or decreasing negative Vb2. The reduction of the output error rates can be realized effectively by increasing the driving voltage (Vdd).

  • Research on Stability of MMC-Based Medium Voltage DC Bus on Ships Based on Lyapunov Method Open Access

    Liang FANG  Xiaoyan XU  Tomasz TARASIUK  

     
    PAPER

      Pubricized:
    2022/05/09
      Vol:
    E105-C No:11
      Page(s):
    675-683

    Modular multilevel converters (MMCs) are an emerging and promising option for medium voltage direct current (MVDC) of all- electric ships. In order to improve the stability of the MVDC transmission system for ships, this paper presents a new control inputs-based Lyapunov strategy based on feedback linearization. Firstly, a set of dynamics equations is proposed based on separating the dynamics of AC-part currents and MMCs circulating currents. The new control inputs can be obtained by the use of feedback linearization theory applied to the dynamic equations. To complete the dynamic parts of the new control inputs from the viewpoint of MVDC system stability, the Lyapunov theory is designed some compensators to demonstrate the effects of the new control inputs on the MMCs state variable errors and its dynamic. In addition, the carrier phase shifted modulation strategy is used because of applying the few number of converter modules to the MVDC system for ships. Moreover, relying on the proposed control strategy, a simulation model is built in MATLAB/SIMULINK software, where simulation results are utilized to verify the validity of proposed control strategy in the MMC-based MVDC system for ships.

  • Present Status and Prospect of Graphene Interconnect Applications

    Kazuyoshi UENO  

     
    PAPER

      Pubricized:
    2022/04/21
      Vol:
    E105-C No:10
      Page(s):
    572-577

    Graphene has been expected as an alternative material for copper interconnects in which resistance increases and reliability deteriorates in nanoscale. While the principle advantages are verified by simulations and experiments, they have not been put into practical use due to the immaturity of the manufacturing process leading to mass production. On the other hand, recent steady progress in the fabrication process has increased the possibility of practical application. In this paper, I will review the recent advances and the latest prospects for conductor applications of graphene centered on interconnects. The possibility of further application utilizing the unique characteristics of graphene is discussed.

  • 28nm Atom-Switch FPGA: Static Timing Analysis and Evaluation

    Xu BAI  Ryusuke NEBASHI  Makoto MIYAMURA  Kazunori FUNAHASHI  Naoki BANNO  Koichiro OKAMOTO  Hideaki NUMATA  Noriyuki IGUCHI  Tadahiko SUGIBAYASHI  Toshitsugu SAKAMOTO  Munehiro TADA  

     
    BRIEF PAPER

      Pubricized:
    2022/06/27
      Vol:
    E105-C No:10
      Page(s):
    627-630

    A static timing analysis (STA) tool for a 28nm atom-switch FPGA (AS-FPGA) is introduced to validate the signal delay of an application circuit before implementation. High accuracy of the STA tool is confirmed by implementing a practical application circuit on the 28nm AS-FPGA. Moreover, dramatic improvement of delay and power is demonstrated in comparison with a previous 40nm AS-FPGA.

  • Geometric Partitioning Mode with Inter and Intra Prediction for Beyond Versatile Video Coding

    Yoshitaka KIDANI  Haruhisa KATO  Kei KAWAMURA  Hiroshi WATANABE  

     
    PAPER

      Pubricized:
    2022/06/21
      Vol:
    E105-D No:10
      Page(s):
    1691-1703

    Geometric partitioning mode (GPM) is a new inter prediction tool adopted in versatile video coding (VVC), which is the latest video coding of international standard developed by joint video expert team in 2020. Different from the regular inter prediction performed on rectangular blocks, GPM separates a coding block into two regions by the pre-defined 64 types of straight lines, generates inter predicted samples for each separated region, and then blends them to obtain the final inter predicted samples. With this feature, GPM improves the prediction accuracy at the boundary between the foreground and background with different motions. However, GPM has room to further improve the prediction accuracy if the final predicted samples can be generated using not only inter prediction but also intra prediction. In this paper, we propose a GPM with inter and intra prediction to achieve further enhanced compression capability beyond VVC. To maximize the coding performance of the proposed method, we also propose the restriction of the applicable intra prediction mode number and the prohibition of applying the intra prediction to both GPM-separated regions. The experimental results show that the proposed method improves the coding performance gain by the conventional GPM method of VVC by 1.3 times, and provides an additional coding performance gain of 1% bitrate savings in one of the coding structures for low-latency video transmission where the conventional GPM method cannot be utilized.

  • Bitstream-Quality-Estimation Model for Tile-Based VR Video Streaming Services Open Access

    Masanori KOIKE  Yuichiro URATA  Kazuhisa YAMAGISHI  

     
    PAPER-Multimedia Systems for Communications

      Pubricized:
    2022/02/18
      Vol:
    E105-B No:8
      Page(s):
    1002-1013

    Tile-based virtual reality (VR) video consists of high-resolution tiles that are displayed in accordance with the users' viewing directions and a low-resolution tile that is the entire VR video and displayed when users change their viewing directions. Whether users perceive quality degradation when watching tile-based VR video depends on high-resolution tile size, the quality of high- and low-resolution tiles, and network condition. The display time of low-resolution tile (hereafter delay) affects users' perceived quality because longer delay makes users watch the low-resolution tiles longer. Since these degradations of low-resolution tiles markedly affect users' perceived quality, these points have to be considered in the quality-estimation model. Therefore, we propose a bitstream-quality-estimation model for tile-based VR video streaming services and investigate the effect of bitstream parameters and delay on tile-based VR video quality. Subjective experiments on several videos of different qualities and a comparison between other video quality-estimation models were conducted. In this paper, we prove that the proposed model can improve the quality-estimation accuracy by using the high- and low-resolution tiles' quantization parameters, resolution, framerate, and delay. Subjective experimental results show that the proposed model can estimate the quality of tile-based VR video more accurately than other video quality-estimation models.

  • A Two-Level Cache Aware Adaptive Data Replication Mechanism for Shared LLC

    Qianqian WU  Zhenzhou JI  

     
    LETTER-Computer System

      Pubricized:
    2022/03/25
      Vol:
    E105-D No:7
      Page(s):
    1320-1324

    The shared last level cache (SLLC) in tile chip multiprocessors (TCMP) provides a low off-chip miss rate, but it causes a long on-chip access latency. In the two-level cache hierarchy, data replication stores replicas of L1 victims in the local LLC (L2 cache) to obtain a short local LLC access latency on the next accesses. Many data replication mechanisms have been proposed, but they do not consider both L1 victim reuse behaviors and LLC replica reception capability. They either produce many useless replicas or increase LLC pressure, which limits the improvement of system performance. In this paper, we propose a two-level cache aware adaptive data replication mechanism (TCDR), which controls replication based on both L1 victim reuse behaviors prediction and LLC replica reception capability monitoring. TCDR not only increases the accuracy of L1 replica selection, but also avoids the pressure of replication on LLC. The results show that TCDR improves the system performance with reasonable hardware overhead.

  • Five Cells and Tilepaint are NP-Complete

    Chuzo IWAMOTO  Tatsuya IDE  

     
    PAPER

      Pubricized:
    2021/10/18
      Vol:
    E105-D No:3
      Page(s):
    508-516

    Five Cells and Tilepaint are Nikoli's pencil puzzles. We study the computational complexity of Five Cells and Tilepaint puzzles. It is shown that deciding whether a given instance of each puzzle has a solution is NP-complete.

  • Research on Dissections of a Net of a Cube into Nets of Cubes

    Tamami OKADA  Ryuhei UEHARA  

     
    PAPER

      Pubricized:
    2021/10/22
      Vol:
    E105-D No:3
      Page(s):
    459-465

    A rep-cube is a polyomino that is a net of a cube, and it can be divided into some polyominoes such that each of them can be folded into a cube. This notion was invented in 2017, which is inspired by the notions of polyomino and rep-tile, which were introduced by Solomon W. Golomb. A rep-cube is called regular if it can be divided into the nets of the same area. A regular rep-cube is of order k if it is divided into k nets. Moreover, it is called uniform if it can be divided into the congruent nets. In this paper, we focus on these special rep-cubes and solve several open problems.

  • Proposal and Evaluation of IO Concentration-Aware Mechanisms to Improve Efficiency of Hybrid Storage Systems

    Kazuichi OE  Takeshi NANRI  

     
    PAPER

      Pubricized:
    2021/07/30
      Vol:
    E104-D No:12
      Page(s):
    2109-2120

    Hybrid storage techniques are useful methods to improve the cost performance for input-output (IO) intensive workloads. These techniques choose areas of concentrated IO accesses and migrate them to an upper tier to extract as much performance as possible through greater use of upper tier areas. Automated tiered storage with fast memory and slow flash storage (ATSMF) is a hybrid storage system situated between non-volatile memories (NVMs) and solid-state drives (SSDs). ATSMF aims to reduce the average response time for IO accesses by migrating areas of concentrated IO access from an SSD to an NVM. When a concentrated IO access finishes, the system migrates these areas from the NVM back to the SSD. Unfortunately, the published ATSMF implementation temporarily consumes much NVM capacity upon migrating concentrated IO access areas to NVM, because its algorithm executes NVM migration with high priority. As a result, it often delays evicting areas in which IO concentrations have ended to the SSD. Therefore, to reduce the consumption of NVM while maintaining the average response time, we developed new techniques for making ATSMF more practical. The first is a queue handling technique based on the number of IO accesses for NVM migration and eviction. The second is an eviction method that selects only write-accessed partial regions in finished areas. The third is a technique for variable eviction timing to balance the NVM consumption and average response time. Experimental results indicate that the average response times of the proposed ATSMF are almost the same as those of the published ATSMF, while the NVM consumption is three times lower in best case.

  • Nonvolatile Field-Programmable Gate Array Using a Standard-Cell-Based Design Flow

    Daisuke SUZUKI  Takahiro HANYU  

     
    PAPER-Logic Design

      Pubricized:
    2021/04/16
      Vol:
    E104-D No:8
      Page(s):
    1111-1120

    A nonvolatile field-programmable gate array (NV-FPGA), where the circuit-configuration information still remains without power supply, offers a powerful solution against the standby power issue. In this paper, an NV-FPGA is proposed where the programmable logic and interconnect function blocks are described in a hardware description language and are pushed through a standard-cell-based design flow with nonvolatile flip-flops. The use of the standard-cell-based design flow makes it possible to migrate any arbitrary process technology and to perform architecture-level simulation with physical information. As a typical example, the proposed NV-FPGA is designed under 55nm CMOS/100nm magnetic tunnel junction (MTJ) technologies, and the performance of the proposed NV-FPGA is evaluated in comparison with that of a CMOS-only volatile FPGA.

  • Energy Efficient Approximate Storing of Image Data for MTJ Based Non-Volatile Flip-Flops and MRAM

    Yoshinori ONO  Kimiyoshi USAMI  

     
    PAPER

      Pubricized:
    2021/01/06
      Vol:
    E104-C No:7
      Page(s):
    338-349

    A non-volatile memory (NVM) employing MTJ has a lot of strong points such as read/write performance, best endurance and operating-voltage compatibility with standard CMOS. However, it consumes a lot of energy when writing the data. This becomes an obstacle when applying to battery-operated mobile devices. To solve this problem, we propose an approach to augment the capability of the precision scaling technique for the write operation in NVM. Precision scaling is an approximate computing technique to reduce the bit width of data (i.e. precision) for energy reduction. When writing image data to NVM with the precision scaling, the write energy and the image quality are changed according to the write time and the target bit range. We propose an energy-efficient approximate storing scheme for non-volatile flip-flops and a magnetic random-access memory (MRAM) that allows us to write the data by optimizing the bit positions to split the data and the write time for each bit range. By using the statistical model, we obtained optimal values for the write time and the targeted bit range under the trade-off between the write energy reduction and image quality degradation. Simulation results have demonstrated that by using these optimal values the write energy can be reduced up to 50% while maintaining the acceptable image quality. We also investigated the relationship between the input images and the output image quality when using this approach in detail. In addition, we evaluated the energy benefits when applying our approach to nine types of image processing including linear filters and edge detectors. Results showed that the write energy is reduced by further 12.5% at the maximum.

  • Recovering Faulty Non-Volatile Flip Flops for Coarse-Grained Reconfigurable Architectures

    Takeharu IKEZOE  Takuya KOJIMA  Hideharu AMANO  

     
    PAPER

      Pubricized:
    2020/12/14
      Vol:
    E104-C No:6
      Page(s):
    215-225

    Recent IoT devices require extremely low standby power consumption, while a certain performance is needed during the active time, and Coarse-Grained Reconfigurable Arrays (CGRAs) have received attention because of their high energy efficiency. For further reduction of the standby energy consumption of CGRAs, the leakage power for their configuration memory must be reduced. Although the power gating is a common technique, the lost data in flip-flops and memory must be retrieved after the wake-up. Recovering everything requires numerous state transitions and considerable overhead both on its execution time and energy. To address the problem, Non-volatile Cool Mega Array (NVCMA), a CGRA providing non-volatile flip-flops (NVFFs) with spin transfer torque type non-volatile memory (NVM) technology has been developed. However, in general, non-volatile memory technologies have problems with reliability. Some NVFFs are stacked-at-0/1, and cannot store the data in a certain possibility. To improve the chip yield, we propose a mapping algorithm to avoid faulty processing elements of the CGRA caused by the erroneous configuration data. Next, we also propose a method to add an error-correcting code (ECC) mechanism to NVFFs for the configuration and constant memory. The proposed method was applied to NVCMA to evaluate the availability rate and reduction of write time. By using both methods, the average availability ratio of 94.2% was achieved, while the average availability ratio of the nine applications was 0.056% when the probability of failure of the FF was 0.01. The energy for storing data becomes about 2.3 times because of the hardware overhead of ECC but the proposed method can save 8.6% of the writing power on average.

1-20hit(168hit)