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[Keyword] ASE(2849hit)

181-200hit(2849hit)

  • A Simple Depth-Key-Based Image Composition Considering Object Movement in Depth Direction

    Mami NAGOYA  Tomoaki KIMURA  Hiroyuki TSUJI  

     
    LETTER-Computer Graphics

      Vol:
    E103-A No:12
      Page(s):
    1603-1608

    A simple depth-key-based image composition is proposed, which uses two still images with depth information, background and foreground object. The proposed method can place the object at various locations in the background considering the depth in the 3D world coordinate system. The main feature is that a simple algorithm is provided, which enables us to achieve the depthward movement within the camera plane, without being aware of the 3D world coordinate system. Two algorithms are proposed (P-OMDD and O-OMDD), which are based on the pin-hole camera model. As an advantage, camera calibration is not required before applying the algorithm in these methods. Since a single image is used for the object representation, each of the proposed methods has its limitations in terms of fidelity of the composite image. P-OMDD faithfully reproduces the angle at which the object is seen, but the pixels of the hidden surface are missing. On the contrary, O-OMDD can avoid the hidden surface problem, but the angle of the object is fixed, wherever it moves. It is verified through several experiments that, when using O-OMDD, subjectively natural composite images can be obtained under any object movement, in terms of size and position in the camera plane. Future tasks include improving the change in illumination due to positional changes and the partial loss of objects due to noise in depth images.

  • Design and Implementation of Personalized Integrated Broadcast — Broadband Service in Terrestrial Networks

    Nayeon KIM  Woongsoo NA  Byungjun BAE  

     
    LETTER-Systems and Control

      Vol:
    E103-A No:12
      Page(s):
    1621-1623

    This article proposes a dynamic linkage service which is a specific service model of integrated broadcast — broadband services based ATSC 3.0. The dynamic linkage service is useful to the viewer who wants to continue watching programs using TV or their personal devices, even after the terrestrial broadcast ends due to the start of the next regular programming. In addition, we verify the feasibility of the proposed extended dynamic linkage service through developed emulation system based on ATSC 3.0. In consideration of the personal network capabilities of the viewer environment, the service was tested with 4K/2K Ultra HD and receiving the service was finished within 4 second over intranet.

  • Theoretical Analyses of Maximum Cyclic Autocorrelation Selection Based Spectrum Sensing

    Shusuke NARIEDA  Daiki CHO  Hiromichi OGASAWARA  Kenta UMEBAYASHI  Takeo FUJII  Hiroshi NARUSE  

     
    PAPER-Terrestrial Wireless Communication/Broadcasting Technologies

      Pubricized:
    2020/06/22
      Vol:
    E103-B No:12
      Page(s):
    1462-1469

    This paper provides theoretical analyses for maximum cyclic autocorrelation selection (MCAS)-based spectrum sensing techniques in cognitive radio networks. The MCAS-based spectrum sensing techniques are low computational complexity spectrum sensing in comparison with some cyclostationary detection. However, MCAS-based spectrum sensing characteristics have never been theoretically derived. In this study, we derive closed form solutions for signal detection probability and false alarm probability for MCAS-based spectrum sensing. The theoretical values are compared with numerical examples, and the values match well with each other.

  • Online Signature Verification Using Single-Template Matching Through Locally and Globally Weighted Dynamic Time Warping

    Manabu OKAWA  

     
    PAPER-Image Recognition, Computer Vision

      Pubricized:
    2020/09/01
      Vol:
    E103-D No:12
      Page(s):
    2701-2708

    In this paper, we propose a novel single-template strategy based on a mean template set and locally/globally weighted dynamic time warping (LG-DTW) to improve the performance of online signature verification. Specifically, in the enrollment phase, we implement a time series averaging method, Euclidean barycenter-based DTW barycenter averaging, to obtain a mean template set considering intra-user variability among reference samples. Then, we acquire a local weighting estimate considering a local stability sequence that is obtained analyzing multiple matching points of an optimal match between the mean template and reference sets. Thereafter, we derive a global weighting estimate based on the variable importance estimated by gradient boosting. Finally, in the verification phase, we apply both local and global weighting methods to acquire a discriminative LG-DTW distance between the mean template set and a query sample. Experimental results obtained on the public SVC2004 Task2 and MCYT-100 signature datasets confirm the effectiveness of the proposed method for online signature verification.

  • Inpainting via Sparse Representation Based on a Phaseless Quality Metric

    Takahiro OGAWA  Keisuke MAEDA  Miki HASEYAMA  

     
    PAPER-Image

      Vol:
    E103-A No:12
      Page(s):
    1541-1551

    An inpainting method via sparse representation based on a new phaseless quality metric is presented in this paper. Since power spectra, phaseless features, of local regions within images enable more successful representation of their texture characteristics compared to their pixel values, a new quality metric based on these phaseless features is newly derived for image representation. Specifically, the proposed method enables spare representation of target signals, i.e., target patches, including missing intensities by monitoring errors converged by phase retrieval as the novel phaseless quality metric. This is the main contribution of our study. In this approach, the phase retrieval algorithm used in our method has the following two important roles: (1) derivation of the new quality metric that can be derived even for images including missing intensities and (2) conversion of phaseless features, i.e., power spectra, to pixel values, i.e., intensities. Therefore, the above novel approach solves the existing problem of not being able to use better features or better quality metrics for inpainting. Results of experiments showed that the proposed method using sparse representation based on the new phaseless quality metric outperforms previously reported methods that directly use pixel values for inpainting.

  • Novel Multi-Objective Design Approach for Cantilever of Relay Contact Using Preference Set-Based Design Method

    Yoshiki KAYANO  Kazuaki MIYANAGA  Hiroshi INOUE  

     
    BRIEF PAPER

      Pubricized:
    2020/07/03
      Vol:
    E103-C No:12
      Page(s):
    713-717

    In the design of electrical contacts, it is required to pursue a solution which satisfies simultaneously multi-objective (electrical, mechanical, and thermal) performances including conflicting requirements. Preference Set-Based Design (PSD) has been proposed as practical procedure of the fuzzy set-based design method. This brief paper newly attempts to propose a concurrent design method by PSD to electrical contact, specifically a design of a shape of cantilever in relay contacts. In order to reduce the calculation (and/or experimental) cost, this paper newly attempt to apply Design of Experiments (DoE) for meta-modeling to PSD. The number of the calculation for the meta-modeling can be reduced to $ rac{1}{729}$ by using DoE. The design parameters (width and length) of a cantilever for drive an electrical contact, which satisfy required performance (target deflection), are obtained in ranges successfully by PSD. The validity of the design parameters is demonstrated by numerical modeling.

  • Practical Card-Based Protocol for Three-Input Majority Open Access

    Kenji YASUNAGA  

     
    LETTER-Cryptography and Information Security

      Pubricized:
    2020/05/14
      Vol:
    E103-A No:11
      Page(s):
    1296-1298

    We present a card-based protocol for computing a three-input majority using six cards. The protocol essentially consists of performing a simple XOR protocol two times. Compared to the existing protocols, our protocol does not require private operations other than choosing cards.

  • Example Phrase Adaptation Method for Customized, Example-Based Dialog System Using User Data and Distributed Word Representations

    Norihide KITAOKA  Eichi SETO  Ryota NISHIMURA  

     
    PAPER-Speech and Hearing

      Pubricized:
    2020/07/30
      Vol:
    E103-D No:11
      Page(s):
    2332-2339

    We have developed an adaptation method which allows the customization of example-based dialog systems for individual users by applying “plus” and “minus” operations to the distributed representations obtained using the word2vec method. After retrieving user-related profile information from the Web, named entity extraction is applied to the retrieval results. Words with a high term frequency-inverse document frequency (TF-IDF) score are then adopted as user related words. Next, we calculate the similarity between the distrubuted representations of selected user-related words and nouns in the existing example phrases, using word2vec embedding. We then generate phrases adapted to the user by substituting user-related words for highly similar words in the original example phrases. Word2vec also has a special property which allows the arithmetic operations “plus” and “minus” to be applied to distributed word representations. By applying these operations to words used in the original phrases, we are able to determine which user-related words can be used to replace the original words. The user-related words are then substituted to create customized example phrases. We evaluated the naturalness of the generated phrases and found that the system could generate natural phrases.

  • Non-Linear Distance Filter for Modeling Effect of a Large Pointer Used in a Gesture-Based Pointing Interface

    Kazuaki KONDO  Takuto FUJIWARA  Yuichi NAKAMURA  

     
    PAPER-Human-computer Interaction

      Pubricized:
    2020/08/03
      Vol:
    E103-D No:11
      Page(s):
    2302-2313

    When using a gesture-based interface for pointing to targets on a wide screen, displaying a large pointer instead of a typical spot pattern reduces disturbance caused by measurement errors of user's pointing posture. However, it remains unclear why a large pointer helps facilitate easy pointing. To examine this issue, in this study we propose a mathematical model that formulates human pointing motions affected by a large pointer. Our idea is to describe the effect of the large pointer as human visual perception, because the user will perceive the pointer-target distance as being shorter than it actually is. We embedded this scheme, referred to as non-linear distance filter (NDF), into a typical feedback loop model designed to formulate human pointing motions. We also proposed a method to estimate NDF mapping from pointing trajectories, and used it to investigate the applicability of the model under three typical disturbance patterns: small vibration, smooth shift, and step signal. Experimental results demonstrated that the proposed NDF-based model could accurately reproduced actual pointing trajectories, achieving high similarity values of 0.89, 0.97, and 0.91 for the three respective disturbance patterns. The results indicate the applicability of the proposed method. In addition, we confirmed that the obtained NDF mappings suggested rationales for why a large pointer helps facilitate easy pointing.

  • PPLN-Based Low-Noise Phase Sensitive Amplification Using an Optical Phase-Locked Pump Open Access

    Takushi KAZAMA  Takeshi UMEKI  Yasuhiro OKAMURA  Koji ENBUTSU  Osamu TADANAGA  Atsushi TAKADA  Ryoichi KASAHARA  

     
    PAPER

      Pubricized:
    2020/05/22
      Vol:
    E103-B No:11
      Page(s):
    1265-1271

    We evaluated the noise properties of a periodically poled lithium niobite phase-sensitive amplifier (PSA) using a phase-locked local oscillator as a pump generated by an optical phase-locked loop (OPLL-LO). To examine whether or not the LO pump generated by an OPLL degrades the noise figure (NF) of the PSA, we compared the noise levels of a PSA using an OPLL-LO with that of one using a master local oscillator (M-LO) that utilizes the master light itself as a pump in the electrical domain. With the OPLL, the phase-locked local light had almost the same frequency noise components as the master light. We observed almost the same output noise spectra for the OPLL-LO PSA and M-LO PSA and confirmed the absence of excess noise components in the OPLL-LO PSA in the 0.1 to 20-GHz range. The OPLL-LO PSA exhibited low-noise amplification with an average NF of 1.7-dB at a 23.2-dB gain within an input power range of -31 to -21dBm, which is a feasible input power for repeater amplifiers used in the optical signal transmission systems. We also investigated the influence of the noisy master light, which emulates the accumulation of optical noise from the amplifiers in the transmission system. The OPLL-LO PSA was highly tolerant to the optical noise because the difference in the NF was negligibly small within a master light OSNR range of 5 to 55dB. These results indicate that the OPLL-LO PSA will be useful as a low-noise repeater amplifier for the spectrally efficient large-capacity photonic networks of the future.

  • Nonlinearity Mitigation of PDM-16QAM Signals Using Multiple CSI-OPCs in Ultra-Long-Haul Transmission without Excess Penalty Open Access

    Takeshi UMEKI  Takayuki KOBAYASHI  Akihide SANO  Takuya IKUTA  Masashi ABE  Takushi KAZAMA  Koji ENBUTSU  Ryoichi KASAHARA  Yutaka MIYAMOTO  

     
    PAPER

      Pubricized:
    2020/05/22
      Vol:
    E103-B No:11
      Page(s):
    1226-1232

    We developed a polarization-independent and reserved-band-less complementary spectral inverted optical phase conjugation (CSI-OPC) device using dual-band difference frequency generation based on highly efficient periodically poled LiNbO3 waveguide technologies. To examine the nonlinearity mitigation in a long-haul transmission using a large number of OPCs, we installed a CSI-OPC device in the middle of a pure silica core fiber-based recirculating loop transmission line with a length of 320km. First, we examined the fiber-input power tolerance after 5,120-km and 6,400-km transmission using 22.5-Gbaud PDM-16QAM 10-channel DWDM signals and found a Q-factor improvement of over 1.3dB along with enhanced power tolerance thanks to mitigating the fiber nonlinearity. We then demonstrated transmission distance extension using the CSI-OPC device. The use of multiple CSI-OPCs enables an obvious performance improvements attained by extending the transmission distance from 6,400km to 8,960km, which corresponds to applying the CSI-OPC device 28 times. Moreover, there was no Q-factor degradation for the link in a linear regime after applying the CSI-OPC device more than 16 times. These results demonstrate that the CSI-OPC device can improve the nonlinear tolerance of PDM-16QAM signals without an excess penalty.

  • A Constant-Time Algorithm of CSIDH Keeping Two Points Open Access

    Hiroshi ONUKI  Yusuke AIKAWA  Tsutomu YAMAZAKI  Tsuyoshi TAKAGI  

     
    PAPER-cryptography

      Vol:
    E103-A No:10
      Page(s):
    1174-1182

    At ASIACRYPT 2018, Castryck, Lange, Martindale, Panny and Renes proposed CSIDH, which is a key-exchange protocol based on isogenies between elliptic curves, and a candidate for post-quantum cryptography. However, the implementation by Castryck et al. is not constant-time. Specifically, a part of the secret key could be recovered by the side-channel attacks. Recently, Meyer, Campos, and Reith proposed a constant-time implementation of CSIDH by introducing dummy isogenies and taking secret exponents only from intervals of non-negative integers. Their non-negative intervals make the calculation cost of their implementation of CSIDH twice that of the worst case of the standard (variable-time) implementation of CSIDH. In this paper, we propose a more efficient constant-time algorithm that takes secret exponents from intervals symmetric with respect to the zero. For using these intervals, we need to keep two torsion points on an elliptic curve and calculation for these points. We evaluate the costs of our implementation and that of Meyer et al. in terms of the number of operations on a finite prime field. Our evaluation shows that our constant-time implementation of CSIDH reduces the calculation cost by 28% compared with the implementation by Mayer et al. We also implemented our algorithm by extending the implementation in C of Meyer et al. (originally from Castryck et al.). Then our implementation achieved 152 million clock cycles, which is about 29% faster than that of Meyer et al. and confirms the above reduction ratio in our cost evaluation.

  • Complex Orthogonal Variable Spreading Factor Codes Based on Polyphase Sequences Open Access

    Tomoko K. MATSUSHIMA  Shoichiro YAMASAKI  

     
    PAPER-communication

      Vol:
    E103-A No:10
      Page(s):
    1218-1226

    The direct sequence code division multiple access (DS-CDMA) technique is widely used in various communication systems. When adopting orthogonal variable spreading factor (OVSF) codes, DS-CDMA is particularly suitable for supporting multi-user/multi-rate data transmission services. A useful property of OVSF codes is that no two code sequences assigned to different users will ever interfere with each other, even if their spreading factors are different. Conventional OVSF codes are constructed based on binary orthogonal codes, called Walsh codes, and OVSF code sequences are binary sequences. In this paper, we propose new OVSF codes that are constructed based on polyphase orthogonal codes and consist of complex sequences in which each symbol is represented as a complex number. Construction of the proposed codes is based on a tree structure that is similar to conventional OVSF codes. Since the proposed codes are generalized versions of conventional OVSF codes, any conventional OVSF code can be presented as a special case of the proposed codes. Herein, we show the method used to construct the proposed OVSF codes, after which the orthogonality of the codes, including conventional OVSF codes, is investigated. Among the advantages of our proposed OVSF codes is that the spreading factor can be designed more flexibly in each layer than is possible with conventional OVSF codes. Furthermore, combination of the proposed code and a non-binary phase modulation is well suited to DS-CDMA systems where the level fluctuation of signal envelope is required to be suppressed.

  • A Compact TF-Based LC-VCO with Ultra-Low-Power Operation and Supply Pushing Reduction for IoT Applications

    Zheng SUN  Dingxin XU  Hongye HUANG  Zheng LI  Hanli LIU  Bangan LIU  Jian PANG  Teruki SOMEYA  Atsushi SHIRANE  Kenichi OKADA  

     
    PAPER-Electronic Circuits

      Pubricized:
    2020/04/15
      Vol:
    E103-C No:10
      Page(s):
    505-513

    This paper presents a miniaturized transformer-based ultra-low-power (ULP) LC-VCO with embedded supply pushing reduction techniques for IoT applications in 65-nm CMOS process. To reduce the on-chip area, a compact transformer patterned ground shield (PGS) is implemented. The transistors with switchable capacitor banks and associated components are placed underneath the transformer, which further shrinking the on-chip area. To lower the power consumption of VCO, a gm-stacked LC-VCO using the transformer embedded with PGS is proposed. The transformer is designed to provide large inductance to obtain a robust start-up within limited power consumption. Avoiding implementing an off/on-chip Low-dropout regulator (LDO) which requires additional voltage headroom, a low-power supply pushing reduction feedback loop is integrated to mitigate the current variation and thus the oscillation amplitude and frequency can be stabilized. The proposed ULP TF-based LC-VCO achieves phase noise of -114.8dBc/Hz at 1MHz frequency offset and 16kHz flicker corner with a 103µW power consumption at 2.6GHz oscillation frequency, which corresponds to a -193dBc/Hz VCO figure-of-merit (FoM) and only occupies 0.12mm2 on-chip area. The supply pushing is reduced to 2MHz/V resulting in a -50dBc spur, while 5MHz sinusoidal ripples with 50mVPP are added on the DC supply.

  • 0.3 V 15-GHz Band VCO ICs with Novel Transformer-Based Harmonic Tuned Tanks in 45-nm SOI CMOS

    Xiao XU  Tsuyoshi SUGIURA  Toshihiko YOSHIMASU  

     
    PAPER-Microwaves, Millimeter-Waves

      Pubricized:
    2020/04/10
      Vol:
    E103-C No:10
      Page(s):
    417-425

    This paper presents two ultra-low voltage and high performance VCO ICs with two novel transformer-based harmonic tuned tanks. The first proposed harmonic tuned tank effectively shapes the pseudo-square drain-node voltage waveform for close-in phase noise reduction. To compensate the voltage drop caused by the transformer, an improved second tank is proposed. It not only has tuned harmonic impedance but also provides a voltage gain to enlarge the output voltage swing over supply voltage limitation. The VCO with second tank exhibits over 3 dB better phase noise performance in 1/f2 region among all tuning range. The two VCO ICs are designed, fabricated and measured on wafer in 45-nm SOI CMOS technology. With only 0.3 V supply voltage, the proposed two VCO ICs exhibit best phase noise of -123.3 and -127.2 dBc/Hz at 10 MHz offset and related FoMs of -191.7 and -192.2 dBc/Hz, respectively. The frequency tuning ranges of them are from 14.05 to 15.14 GHz and from 14.23 to 15.68 GHz, respectively.

  • Feedback Signal Processing that Improves Accuracy of Velocity and Direction of Arrival Estimation for Automotive Radar

    Saki SUSA TANAKA  Akira KITAYAMA  Yukinori AKAMINE  Hiroshi KURODA  

     
    BRIEF PAPER-Microwaves, Millimeter-Waves

      Pubricized:
    2020/04/17
      Vol:
    E103-C No:10
      Page(s):
    543-546

    For automotive millimeter radar, a method using a multi-input multi-output (MIMO) array antenna is essential for high angle resolution with module miniaturization. MIMO enables us to extend an antenna array with virtual antennas, and a large antenna array aperture enables high resolution angle estimation. Time division multiplex (TDM) MIMO, which is a method to generate virtual array antennas, makes it easy to design radar system integrated circuits. However, this method leads to two issues in signal processing; the phase error reduces the accuracy of angle estimation of a moving target, and the maximum detectable velocity decreases in inverse proportion to the number of Tx antennas. We analytically derived this phase error and proposed a method to correct the error. Because the phase error of TDM-MIMO is proportional to the target velocity, accurate estimation of the target velocity is an important issue for phase error correction. However, the decrease of the maximum detectable velocity in TDM-MIMO reduces the accuracy of both velocity estimation and angle estimation. To solve these issues, we propose new signal processing for range-velocity estimation for TDM-MIMO radar. By using the feedback result of the estimated direction of arrival (DoA), we can avoid decreasing the maximum detectable velocity. We explain our method with our simulation results.

  • Optimal Rejuvenation Policies for Non-Markovian Availability Models with Aperiodic Checkpointing

    Junjun ZHENG  Hiroyuki OKAMURA  Tadashi DOHI  

     
    PAPER-Dependable Computing

      Pubricized:
    2020/07/16
      Vol:
    E103-D No:10
      Page(s):
    2133-2142

    In this paper, we present non-Markovian availability models for capturing the dynamics of system behavior of an operational software system that undergoes aperiodic time-based software rejuvenation and checkpointing. Two availability models with rejuvenation are considered taking account of the procedure after the completion of rollback recovery operation. We further proceed to investigate whether there exists the optimal rejuvenation schedule that maximizes the steady-state system availability, which is derived by means of the phase expansion technique, since the resulting models are not the trivial stochastic models such as semi-Markov process and Markov regenerative process, so that it is hard to solve them by using the common approaches like Laplace-Stieltjes transform and embedded Markov chain techniques. The numerical experiments are conducted to determine the optimal rejuvenation trigger timing maximizing the steady-state system availability for each availability model, and to compare both two models.

  • Local Riesz Pyramid for Faster Phase-Based Video Magnification

    Shoichiro TAKEDA  Megumi ISOGAI  Shinya SHIMIZU  Hideaki KIMATA  

     
    PAPER

      Pubricized:
    2020/06/22
      Vol:
    E103-D No:10
      Page(s):
    2036-2046

    Phase-based video magnification methods can magnify and reveal subtle motion changes invisible to the naked eye. In these methods, each image frame in a video is decomposed into an image pyramid, and subtle motion changes are then detected as local phase changes with arbitrary orientations at each pixel and each pyramid level. One problem with this process is a long computational time to calculate the local phase changes, which makes high-speed processing of video magnification difficult. Recently, a decomposition technique called the Riesz pyramid has been proposed that detects only local phase changes in the dominant orientation. This technique can remove the arbitrariness of orientations and lower the over-completeness, thus achieving high-speed processing. However, as the resolution of input video increases, a large amount of data must be processed, requiring a long computational time. In this paper, we focus on the correlation of local phase changes between adjacent pyramid levels and present a novel decomposition technique called the local Riesz pyramid that enables faster phase-based video magnification by automatically processing the minimum number of sufficient local image areas at several pyramid levels. Through this minimum pyramid processing, our proposed phase-based video magnification method using the local Riesz pyramid achieves good magnification results within a short computational time.

  • Recent Progress on Design Method of Microwave Power Amplifier and Applications for Microwave Heating Open Access

    Toshio ISHIZAKI  Takayuki MATSUMURO  

     
    INVITED PAPER-Microwaves, Millimeter-Waves

      Pubricized:
    2020/03/19
      Vol:
    E103-C No:10
      Page(s):
    404-410

    Recently, GaN devices are often adopted in microwave power amplifiers to improve the performances. And many new design methods of microwave power amplifier were proposed. As a result, a high-efficiency and super compact microwave signal source has become easily available. It opens up the way for new microwave heating systems. In this paper, the recent progress on design methods of microwave power amplifier and the applications for microwave heating are described. In the first, a device model of GaN transistor is explained. An equivalent thermal model is introduced into the electrical non-linear equivalent device model. In the second, an active load-pull (ALP) measurement system to design a high-efficiency power amplifier is explained. The principle of the conventional closed-loop ALP system is explained. To avoid the risk of oscillation for the closed-loop ALP system, novel ALP systems are proposed. In the third, a microwave heating system is explained. The heating system monitors the reflection wave. Then, the frequency of the signal source and the phase difference between antennas are controlled to minimize the reflection wave. Absorption efficiency of more than 90% was obtained by the control of frequency and phase. In the last part, applications for a medical instrument is described.

  • CCA-Secure Leakage-Resilient Identity-Based Encryption without q-Type Assumptions

    Toi TOMITA  Wakaha OGATA  Kaoru KUROSAWA  Ryo KUWAYAMA  

     
    PAPER-cryptography

      Vol:
    E103-A No:10
      Page(s):
    1157-1166

    In this paper, we propose a new leakage-resilient identity-based encryption (IBE) scheme that is secure against chosen-ciphertext attacks (CCA) in the bounded memory leakage model. The security of our scheme is based on the external k-Linear assumption. It is the first CCA-secure leakage-resilient IBE scheme which does not depend on q-type assumptions. The leakage rate 1/10 is achieved under the XDLIN assumption (k=2).

181-200hit(2849hit)