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1081-1100hit(20498hit)

  • Usage Log-Based Testing of Embedded Software and Identification of Dependencies among Environmental Components

    Sooyong JEONG  Sungdeok CHA  Woo Jin LEE  

     
    LETTER-Software Engineering

      Pubricized:
    2021/07/28
      Vol:
    E104-D No:11
      Page(s):
    2011-2014

    Embedded software often interacts with multiple inputs from various sensors whose dependency is often complex or partially known to developers. With incomplete information on dependency, testing is likely to be insufficient in detecting errors. We propose a method to enhance testing coverage of embedded software by identifying subtle and often neglected dependencies using information contained in usage log. Usage log, traditionally used primarily for investigative purpose following accidents, can also make useful contribution during testing of embedded software. Our approach relies on first individually developing behavioral model for each environmental input, performing compositional analysis while identifying feasible but untested dependencies from usage log, and generating additional test cases that correspond to untested or insufficiently tested dependencies. Experimental evaluation was performed on an Android application named Gravity Screen as well as an Arduino-based wearable glove app. Whereas conventional CTM-based testing technique achieved average branch coverage of 26% and 68% on these applications, respectively, proposed technique achieved 100% coverage in both.

  • Joint Wireless and Computational Resource Allocation Based on Hierarchical Game for Mobile Edge Computing

    Weiwei XIA  Zhuorui LAN  Lianfeng SHEN  

     
    PAPER-Network

      Pubricized:
    2021/05/14
      Vol:
    E104-B No:11
      Page(s):
    1395-1407

    In this paper, we propose a hierarchical Stackelberg game based resource allocation algorithm (HGRAA) to jointly allocate the wireless and computational resources of a mobile edge computing (MEC) system. The proposed HGRAA is composed of two levels: the lower-level evolutionary game (LEG) minimizes the cost of mobile terminals (MTs), and the upper-level exact potential game (UEPG) maximizes the utility of MEC servers. At the lower-level, the MTs are divided into delay-sensitive MTs (DSMTs) and non-delay-sensitive MTs (NDSMTs) according to their different quality of service (QoS) requirements. The competition among DSMTs and NDSMTs in different service areas to share the limited available wireless and computational resources is formulated as a dynamic evolutionary game. The dynamic replicator is applied to obtain the evolutionary equilibrium so as to minimize the costs imposed on MTs. At the upper level, the exact potential game is formulated to solve the resource sharing problem among MEC servers and the resource sharing problem is transferred to nonlinear complementarity. The existence of Nash equilibrium (NE) is proved and is obtained through the Karush-Kuhn-Tucker (KKT) condition. Simulations illustrate that substantial performance improvements such as average utility and the resource utilization of MEC servers can be achieved by applying the proposed HGRAA. Moreover, the cost of MTs is significantly lower than other existing algorithms with the increasing size of input data, and the QoS requirements of different kinds of MTs are well guaranteed in terms of average delay and transmission data rate.

  • Analysis of Signal Distribution in ASE-Limited Optical On-Off Keying Direct-Detection Systems

    Hiroki KAWAHARA  Kyo INOUE  Koji IGARASHI  

     
    PAPER-Fiber-Optic Transmission for Communications

      Pubricized:
    2021/05/14
      Vol:
    E104-B No:11
      Page(s):
    1386-1394

    This paper provides on a theoretical and numerical study of the probability density function (PDF) of the on-off keying (OOK) signals in ASE-limited systems. We present simple closed formulas of PDFs for the optical intensity and the received baseband signal. To confirm the validity of our model, the calculation results yielded by the proposed formulas are compared with those of numerical simulations and the conventional Gaussian model. Our theoretical and numerical results confirm that the signal distribution differs from a Gaussian profile. It is also demonstrated that our model can properly evaluate the signal distribution and the resultant BER performance, especially for systems with an optical bandwidth close to the receiver baseband width.

  • Flexible Bayesian Inference by Weight Transfer for Robust Deep Neural Networks

    Thi Thu Thao KHONG  Takashi NAKADA  Yasuhiko NAKASHIMA  

     
    PAPER-Image Recognition, Computer Vision

      Pubricized:
    2021/07/28
      Vol:
    E104-D No:11
      Page(s):
    1981-1991

    Adversarial attacks are viewed as a danger to Deep Neural Networks (DNNs), which reveal a weakness of deep learning models in security-critical applications. Recent findings have been presented adversarial training as an outstanding defense method against adversaries. Nonetheless, adversarial training is a challenge with respect to big datasets and large networks. It is believed that, unless making DNN architectures larger, DNNs would be hard to strengthen the robustness to adversarial examples. In order to avoid iteratively adversarial training, our algorithm is Bayes without Bayesian Learning (BwoBL) that performs the ensemble inference to improve the robustness. As an application of transfer learning, we use learned parameters of pretrained DNNs to build Bayesian Neural Networks (BNNs) and focus on Bayesian inference without costing Bayesian learning. In comparison with no adversarial training, our method is more robust than activation functions designed to enhance adversarial robustness. Moreover, BwoBL can easily integrate into any pretrained DNN, not only Convolutional Neural Networks (CNNs) but also other DNNs, such as Self-Attention Networks (SANs) that outperform convolutional counterparts. BwoBL is also convenient to apply to scaling networks, e.g., ResNet and EfficientNet, with better performance. Especially, our algorithm employs a variety of DNN architectures to construct BNNs against a diversity of adversarial attacks on a large-scale dataset. In particular, under l∞ norm PGD attack of pixel perturbation ε=4/255 with 100 iterations on ImageNet, our proposal in ResNets, SANs, and EfficientNets increase by 58.18% top-5 accuracy on average, which are combined with naturally pretrained ResNets, SANs, and EfficientNets. This enhancement is 62.26% on average below l2 norm C&W attack. The combination of our proposed method with pretrained EfficientNets on both natural and adversarial images (EfficientNet-ADV) drastically boosts the robustness resisting PGD and C&W attacks without additional training. Our EfficientNet-ADV-B7 achieves the cutting-edge top-5 accuracy, which is 92.14% and 94.20% on adversarial ImageNet generated by powerful PGD and C&W attacks, respectively.

  • Verifiable Credential Proof Generation and Verification Model for Decentralized SSI-Based Credit Scoring Data

    Kang Woo CHO  Byeong-Gyu JEONG  Sang Uk SHIN  

     
    PAPER

      Pubricized:
    2021/07/27
      Vol:
    E104-D No:11
      Page(s):
    1857-1868

    The continuous development of the mobile computing environment has led to the emergence of fintech to enable convenient financial transactions in this environment. Previously proposed financial identity services mostly adopted centralized servers that are prone to single-point-of-failure problems and performance bottlenecks. Blockchain-based self-sovereign identity (SSI), which emerged to address this problem, is a technology that solves centralized problems and allows decentralized identification. However, the verifiable credential (VC), a unit of SSI data transactions, guarantees unlimited right to erasure for self-sovereignty. This does not suit the specificity of the financial transaction network, which requires the restriction of the right to erasure for credit evaluation. This paper proposes a model for VC generation and revocation verification for credit scoring data. The proposed model includes double zero knowledge - succinct non-interactive argument of knowledge (zk-SNARK) proof in the VC generation process between the holder and the issuer. In addition, cross-revocation verification takes place between the holder and the verifier. As a result, the proposed model builds a trust platform among the holder, issuer, and verifier while maintaining the decentralized SSI attributes and focusing on the VC life cycle. The model also improves the way in which credit evaluation data are processed as VCs by granting opt-in and the special right to erasure.

  • Provable-Security Analysis of Authenticated Encryption Based on Lesamnta-LW in the Ideal Cipher Model

    Shoichi HIROSE  Hidenori KUWAKADO  Hirotaka YOSHIDA  

     
    PAPER

      Pubricized:
    2021/07/08
      Vol:
    E104-D No:11
      Page(s):
    1894-1901

    Hirose, Kuwakado and Yoshida proposed a nonce-based authenticated encryption scheme Lae0 based on Lesamnta-LW in 2019. Lesamnta-LW is a block-cipher-based iterated hash function included in the ISO/IEC 29192-5 lightweight hash-function standard. They also showed that Lae0 satisfies both privacy and authenticity if the underlying block cipher is a pseudorandom permutation. Unfortunately, their result implies only about 64-bit security for instantiation with the dedicated block cipher of Lesamnta-LW. In this paper, we analyze the security of Lae0 in the ideal cipher model. Our result implies about 120-bit security for instantiation with the block cipher of Lesamnta-LW.

  • Speech Paralinguistic Approach for Detecting Dementia Using Gated Convolutional Neural Network

    Mariana RODRIGUES MAKIUCHI  Tifani WARNITA  Nakamasa INOUE  Koichi SHINODA  Michitaka YOSHIMURA  Momoko KITAZAWA  Kei FUNAKI  Yoko EGUCHI  Taishiro KISHIMOTO  

     
    PAPER-Artificial Intelligence, Data Mining

      Pubricized:
    2021/08/03
      Vol:
    E104-D No:11
      Page(s):
    1930-1940

    We propose a non-invasive and cost-effective method to automatically detect dementia by utilizing solely speech audio data. We extract paralinguistic features for a short speech segment and use Gated Convolutional Neural Networks (GCNN) to classify it into dementia or healthy. We evaluate our method on the Pitt Corpus and on our own dataset, the PROMPT Database. Our method yields the accuracy of 73.1% on the Pitt Corpus using an average of 114 seconds of speech data. In the PROMPT Database, our method yields the accuracy of 74.7% using 4 seconds of speech data and it improves to 80.8% when we use all the patient's speech data. Furthermore, we evaluate our method on a three-class classification problem in which we included the Mild Cognitive Impairment (MCI) class and achieved the accuracy of 60.6% with 40 seconds of speech data.

  • DNN-Based Low-Musical-Noise Single-Channel Speech Enhancement Based on Higher-Order-Moments Matching

    Satoshi MIZOGUCHI  Yuki SAITO  Shinnosuke TAKAMICHI  Hiroshi SARUWATARI  

     
    PAPER-Speech and Hearing

      Pubricized:
    2021/07/30
      Vol:
    E104-D No:11
      Page(s):
    1971-1980

    We propose deep neural network (DNN)-based speech enhancement that reduces musical noise and achieves better auditory impressions. The musical noise is an artifact generated by nonlinear signal processing and negatively affects the auditory impressions. We aim to develop musical-noise-free speech enhancement methods that suppress the musical noise generation and produce perceptually-comfortable enhanced speech. DNN-based speech enhancement using a soft mask achieves high noise reduction but generates musical noise in non-speech regions. Therefore, first, we define kurtosis matching for DNN-based low-musical-noise speech enhancement. Kurtosis is the fourth-order moment and is known to correlate with the amount of musical noise. The kurtosis matching is a penalty term of the DNN training and works to reduce the amount of musical noise. We further extend this scheme to standardized-moment matching. The extended scheme involves using moments whose orders are higher than kurtosis and generalizes the conventional musical-noise-free method based on kurtosis matching. We formulate standardized-moment matching and explore how effectively the higher-order moments reduce the amount of musical noise. Experimental evaluation results 1) demonstrate that kurtosis matching can reduce musical noise without negatively affecting noise suppression and 2) newly reveal that the sixth-moment matching also achieves low-musical-noise speech enhancement as well as kurtosis matching.

  • Smaller Residual Network for Single Image Depth Estimation

    Andi HENDRA  Yasushi KANAZAWA  

     
    PAPER-Image Recognition, Computer Vision

      Pubricized:
    2021/08/17
      Vol:
    E104-D No:11
      Page(s):
    1992-2001

    We propose a new framework for estimating depth information from a single image. Our framework is relatively small and straightforward by employing a two-stage architecture: a residual network and a simple decoder network. Our residual network in this paper is a remodeled of the original ResNet-50 architecture, which consists of only thirty-eight convolution layers in the residual block following by pair of two up-sampling and layers. While the simple decoder network, stack of five convolution layers, accepts the initial depth to be refined as the final output depth. During training, we monitor the loss behavior and adjust the learning rate hyperparameter in order to improve the performance. Furthermore, instead of using a single common pixel-wise loss, we also compute loss based on gradient-direction, and their structure similarity. This setting in our network can significantly reduce the number of network parameters, and simultaneously get a more accurate image depth map. The performance of our approach has been evaluated by conducting both quantitative and qualitative comparisons with several prior related methods on the publicly NYU and KITTI datasets.

  • Detecting Depression from Speech through an Attentive LSTM Network

    Yan ZHAO  Yue XIE  Ruiyu LIANG  Li ZHANG  Li ZHAO  Chengyu LIU  

     
    LETTER-Speech and Hearing

      Pubricized:
    2021/08/24
      Vol:
    E104-D No:11
      Page(s):
    2019-2023

    Depression endangers people's health conditions and affects the social order as a mental disorder. As an efficient diagnosis of depression, automatic depression detection has attracted lots of researcher's interest. This study presents an attention-based Long Short-Term Memory (LSTM) model for depression detection to make full use of the difference between depression and non-depression between timeframes. The proposed model uses frame-level features, which capture the temporal information of depressive speech, to replace traditional statistical features as an input of the LSTM layers. To achieve more multi-dimensional deep feature representations, the LSTM output is then passed on attention layers on both time and feature dimensions. Then, we concat the output of the attention layers and put the fused feature representation into the fully connected layer. At last, the fully connected layer's output is passed on to softmax layer. Experiments conducted on the DAIC-WOZ database demonstrate that the proposed attentive LSTM model achieves an average accuracy rate of 90.2% and outperforms the traditional LSTM network and LSTM with local attention by 0.7% and 2.3%, respectively, which indicates its feasibility.

  • A Hybrid Retinex-Based Algorithm for UAV-Taken Image Enhancement

    Xinran LIU  Zhongju WANG  Long WANG  Chao HUANG  Xiong LUO  

     
    LETTER-Image Processing and Video Processing

      Pubricized:
    2021/08/05
      Vol:
    E104-D No:11
      Page(s):
    2024-2027

    A hybrid Retinex-based image enhancement algorithm is proposed to improve the quality of images captured by unmanned aerial vehicles (UAVs) in this paper. Hyperparameters of the employed multi-scale Retinex with chromaticity preservation (MSRCP) model are automatically tuned via a two-phase evolutionary computing algorithm. In the two-phase optimization algorithm, the Rao-2 algorithm is applied to performing the global search and a solution is obtained by maximizing the objective function. Next, the Nelder-Mead simplex method is used to improve the solution via local search. Real UAV-taken images of bad quality are collected to verify the performance of the proposed algorithm. Meanwhile, four famous image enhancement algorithms, Multi-Scale Retinex, Multi-Scale Retinex with Color Restoration, Automated Multi-Scale Retinex, and MSRCP are utilized as benchmarking methods. Meanwhile, two commonly used evolutionary computing algorithms, particle swarm optimization and flower pollination algorithm, are considered to verify the efficiency of the proposed method in tuning parameters of the MSRCP model. Experimental results demonstrate that the proposed method achieves the best performance compared with benchmarks and thus the proposed method is applicable for real UAV-based applications.

  • Distributed Optimal Estimation with Scalable Communication Cost

    Ryosuke ADACHI  Yuh YAMASHITA  Koichi KOBAYASHI  

     
    PAPER

      Pubricized:
    2021/05/18
      Vol:
    E104-A No:11
      Page(s):
    1470-1476

    This paper addresses distributed optimal estimation over wireless sensor networks with scalable communications. For realizing scalable communication, a data-aggregation method is introduced. Since our previously proposed method cannot guarantee the global optimality of each estimator, a modified protocol is proposed. A modification of the proposed method is that weights are introduced in the data aggregation. For selecting the weight values in the data aggregation, a redundant output reduction method with minimum covariance is discussed. Based on the proposed protocol, all estimators can calculate the optimal estimate. Finally, numerical simulations show that the proposed method can realize both the scalability of communication and high accuracy estimation.

  • Neural Network Calculations at the Speed of Light Using Optical Vector-Matrix Multiplication and Optoelectronic Activation

    Naoki HATTORI  Jun SHIOMI  Yutaka MASUDA  Tohru ISHIHARA  Akihiko SHINYA  Masaya NOTOMI  

     
    PAPER

      Pubricized:
    2021/05/17
      Vol:
    E104-A No:11
      Page(s):
    1477-1487

    With the rapid progress of the integrated nanophotonics technology, the optical neural network architecture has been widely investigated. Since the optical neural network can complete the inference processing just by propagating the optical signal in the network, it is expected more than one order of magnitude faster than the electronics-only implementation of artificial neural networks (ANN). In this paper, we first propose an optical vector-matrix multiplication (VMM) circuit using wavelength division multiplexing, which enables inference processing at the speed of light with ultra-wideband. This paper next proposes optoelectronic circuit implementation for batch normalization and activation function, which significantly improves the accuracy of the inference processing without sacrificing the speed performance. Finally, using a virtual environment for machine learning and an optoelectronic circuit simulator, we demonstrate the ultra-fast and accurate operation of the optical-electronic ANN circuit.

  • A Two-Stage Hardware Trojan Detection Method Considering the Trojan Probability of Neighbor Nets

    Kento HASEGAWA  Tomotaka INOUE  Nozomu TOGAWA  

     
    PAPER

      Pubricized:
    2021/05/12
      Vol:
    E104-A No:11
      Page(s):
    1516-1525

    Due to the rapid growth of the information industry, various Internet of Things (IoT) devices have been widely used in our daily lives. Since the demand for low-cost and high-performance hardware devices has increased, malicious third-party vendors may insert malicious circuits into the products to degrade their performance or to leak secret information stored at the devices. The malicious circuit surreptitiously inserted into the hardware products is known as a ‘hardware Trojan.’ How to detect hardware Trojans becomes a significant concern in recent hardware production. In this paper, we propose a hardware Trojan detection method that employs two-stage neural networks and effectively utilizes the Trojan probability of neighbor nets. At the first stage, the 11 Trojan features are extracted from the nets in a given netlist, and then we estimate the Trojan probability that shows the probability of the Trojan nets. At the second stage, we learn the Trojan probability of the neighbor nets for each net in the netlist and classify the nets into a set of normal nets and Trojan ones. The experimental results demonstrate that the average true positive rate becomes 83.6%, and the average true negative rate becomes 96.5%, which is sufficiently high compared to the existing methods.

  • Analysis and Acceleration of the Quadratic Knapsack Problem on an Ising Machine Open Access

    Matthieu PARIZY  Nozomu TOGAWA  

     
    PAPER

      Pubricized:
    2021/07/08
      Vol:
    E104-A No:11
      Page(s):
    1526-1535

    The binary quadratic knapsack problem (QKP) aims at optimizing a quadratic cost function within a single knapsack. Its applications and difficulty make it appealing for various industrial fields. In this paper we present an efficient strategy to solve the problem by modeling it as an Ising spin model using an Ising machine to search for its ground state which translates to the optimal solution of the problem. Secondly, in order to facilitate the search, we propose a novel technique to visualize the landscape of the search and demonstrate how difficult it is to solve QKP on an Ising machine. Finally, we propose two software solution improvement algorithms to efficiently solve QKP on an Ising machine.

  • An Analysis of Local BTI Variation with Ring-Oscillator in Advanced Processes and Its Impact on Logic Circuit and SRAM

    Mitsuhiko IGARASHI  Yuuki UCHIDA  Yoshio TAKAZAWA  Makoto YABUUCHI  Yasumasa TSUKAMOTO  Koji SHIBUTANI  Kazutoshi KOBAYASHI  

     
    PAPER

      Pubricized:
    2021/05/25
      Vol:
    E104-A No:11
      Page(s):
    1536-1545

    In this paper, we present an analysis of local variability of bias temperature instability (BTI) by measuring Ring-Oscillators (RO) on various processes and its impact on logic circuit and SRAM. The evaluation results based on measuring ROs of a test elementary group (TEG) fabricated in 7nm Fin Field Effect Transistor (FinFET) process, 16/14nm generation FinFET processes and a 28nm planer process show that the standard deviations of Negative BTI (NBTI) Vth degradation (σ(ΔVthp)) are proportional to the square root of the mean value (µ(ΔVthp)) at any stress time, Vth flavors and various recovery conditions. While the amount of local BTI variation depends on the gate length, width and number of fins, the amount of local BTI variation at the 7nm FinFET process is slightly larger than other processes. Based on these measurement results, we present an analysis result of its impact on logic circuit considering measured Vth dependency on global NBTI in the 7nm FinFET process. We also analyse its impact on SRAM minimum operation voltage (Vmin) of static noise margin (SNM) based on sensitivity analysis and shows non-negligible Vmin degradation caused by local NBTI.

  • A Synthesis Method Based on Multi-Stage Optimization for Power-Efficient Integrated Optical Logic Circuits

    Ryosuke MATSUO  Jun SHIOMI  Tohru ISHIHARA  Hidetoshi ONODERA  Akihiko SHINYA  Masaya NOTOMI  

     
    PAPER

      Pubricized:
    2021/05/18
      Vol:
    E104-A No:11
      Page(s):
    1546-1554

    Optical logic circuits based on integrated nanophotonics attract significant interest due to their ultra-high-speed operation. However, the power dissipation of conventional optical logic circuits is exponential to the number of inputs of target logic functions. This paper proposes a synthesis method reducing power dissipation to a polynomial order of the number of inputs while exploiting the high-speed nature. Our method divides the target logic function into multiple sub-functions with Optical-to-Electrical (OE) converters. Each sub-function has a smaller number of inputs than that of the original function, which enables to exponentially reduce the power dissipated by an optical logic circuit representing the sub-function. The proposed synthesis method can mitigate the OE converter delay overhead by parallelizing sub-functions. We apply the proposed synthesis method to the ISCAS'85 benchmark circuits. The power consumption of the conventional circuits based on the Binary Decision Diagram (BDD) is at least three orders of magnitude larger than that of the optical logic circuits synthesized by the proposed method. The proposed method reduces the power consumption to about 100mW. The delay of almost all the circuits synthesized by the proposed method is kept less than four times the delay of the conventional BDD-based circuit.

  • An Anomalous Behavior Detection Method Utilizing Extracted Application-Specific Power Behaviors

    Kazunari TAKASAKI  Ryoichi KIDA  Nozomu TOGAWA  

     
    PAPER

      Pubricized:
    2021/07/08
      Vol:
    E104-A No:11
      Page(s):
    1555-1565

    With the widespread use of Internet of Things (IoT) devices in recent years, we utilize a variety of hardware devices in our daily life. On the other hand, hardware security issues are emerging. Power analysis is one of the methods to detect anomalous behaviors, but it is hard to apply it to IoT devices where an operating system and various software programs are running. In this paper, we propose an anomalous behavior detection method for an IoT device by extracting application-specific power behaviors. First, we measure power consumption of an IoT device, and obtain the power waveform. Next, we extract an application-specific power waveform by eliminating a steady factor from the obtained power waveform. Finally, we extract feature values from the application-specific power waveform and detect an anomalous behavior by utilizing the local outlier factor (LOF) method. We conduct two experiments to show how our proposed method works: one runs three application programs and an anomalous application program randomly and the other runs three application programs in series and an anomalous application program very rarely. Application programs on both experiments are implemented on a single board computer. The experimental results demonstrate that the proposed method successfully detects anomalous behaviors by extracting application-specific power behaviors, while the existing approaches cannot.

  • Supply and Threshold Voltage Scaling for Minimum Energy Operation over a Wide Operating Performance Region

    Shoya SONODA  Jun SHIOMI  Hidetoshi ONODERA  

     
    PAPER

      Pubricized:
    2021/05/14
      Vol:
    E104-A No:11
      Page(s):
    1566-1576

    A method for runtime energy optimization based on the supply voltage (Vdd) and the threshold voltage (Vth) scaling is proposed. This paper refers to the optimal voltage pair, which minimizes the energy consumption of LSI circuits under a target delay constraint, as a Minimum Energy Point (MEP). The MEP dynamically fluctuates depending on the operating conditions determined by a target delay constraint, an activity factor and a chip temperature. In order to track the MEP, this paper proposes a closed-form continuous function that determines the MEP over a wide operating performance region ranging from the above-threshold region down to the sub-threshold region. Based on the MEP determination formula, an MEP tracking algorithm is also proposed. The MEP tracking algorithm estimates the MEP even though the operating conditions widely change. Measurement results based on a 32-bit RISC processor fabricated in a 65-nm Silicon On Thin Buried oxide (SOTB) process technology show that the proposed method estimates the MEP within a 5% energy loss in comparison with the actual MEP operation.

  • A Modulus Factorization Algorithm for Self-Orthogonal and Self-Dual Quasi-Cyclic Codes via Polynomial Matrices Open Access

    Hajime MATSUI  

     
    LETTER-Coding Theory

      Pubricized:
    2021/05/21
      Vol:
    E104-A No:11
      Page(s):
    1649-1653

    A construction method of self-orthogonal and self-dual quasi-cyclic codes is shown which relies on factorization of modulus polynomials for cyclicity in this study. The smaller-size generator polynomial matrices are used instead of the generator matrices as linear codes. An algorithm based on Chinese remainder theorem finds the generator polynomial matrix on the original modulus from the ones constructed on each factor. This method enables us to efficiently construct and search these codes when factoring modulus polynomials into reciprocal polynomials.

1081-1100hit(20498hit)