In this paper, the analytical results of the bit error probabilities of convolutional codes using constant Log-MAP decoding by closed-form are presented, and the analytical results are compared with the Max-Log-MAP decoding results. Furthermore, theoretical improvement employing the correction term, which corrects errors induced by the maximum approximation, is shown. The results show that the bit error probability of constant Log-MAP decoding is marginally better than that of Max-LogMAP decoding.

The Viterbi algorithm is widely applied for the decoding of the convolutional codes. But the complexity is increase rapidly in the constraint length. The K-best Viterbi decoding algorithm for the convolutional codes is proposed to reduce its decoding complexity. This is expected to apply for Internet of Things(IoT) devices which are low-scale and low-power hardwares. The author have already shown that the exact bit error performance of Viterbi decoding algorithm for convolutional codes. This analytical technique employs the iterative calculation of probability density function of path metrics. In this paper, the application for error performance analysis for K-best Viterbi decoding algorithm is demonstrated.

The Rabin cryptosystem has been proposed protect the unique ID (UID) in radio-frequency identification tags. The Rabin cryptosystem is a type of lightweight public key system that is theoretically quite secure; however it is vulnerable to several side-channel attacks. In this paper, a crashing modulus attack is presented as a new fault attack on modular squaring during Rabin encryption. This attack requires only one fault in the public key if its perturbed public key can be factored. Our simulation results indicate that the attack is more than 50 percent successful with several faults in practical time. A complicated situation arises when reconstructing the message, including the UID, from ciphertext, i.e., the message and the perturbed public key are not relatively prime. We present a complete and mathematically rigorous message reconstruction algorithm for such a case. Moreover, we propose an exact formula to obtain a number of candidate messages. We show that the number is not generally equal to a power of two.

A new fault attack, double counting attack (DCA), on the precomputation of 2t-ary modular exponentiation for a classical RSA digital signature (i.e., RSA without the Chinese remainder theorem) is proposed. The 2t-ary method is the most popular and widely used algorithm to speed up the RSA signature process. Developers can realize the fastest signature process by choosing optimum t . For example, t=6 is optimum for a 1536-bit classical RSA implementation. The 2t-ary method requires precomputation to generate small exponentials of message. Conventional fault attack research has paid little attention to precomputation, even though precomputation could be a target of a fault attack. The proposed DCA induces faults in precomputation using instruction skip technique, which is equivalent to replacing an instruction with a no operation in assembly language. This paper also presents a useful position checker tool to determine the position of the 2t-ary coefficients of the secret exponent from signatures based on faulted precomputations. The DCA is demonstrated to be an effective attack method for some widely used parameters. DCA can reconstruct an entire secret exponent using the position checker with 63=26-1) faulted signatures in a short time for a 1536-bit RSA implementation using the2t-ary method. The DCA process can be accelerated for a small public exponent (e.g., 65537). To the best of our knowledge, the proposed DCA is the first fault attack against classical RSA precomputation.

In this paper, an analytical result of bit error probability of 2-state convolutional code with log-maximum a posteriori probability (Log-MAP) decoding algorithm with hard decision are presented. The result shows that the error performance of Log-MAP decoding is slightly better than both Max-Log-MAP decoding and Viterbi decoding. Furthermore, the analytical result of bit error probability of 4-level soft decision Log-MAP decoding is shown.

In this paper, a theoretical analysis of bit error probability for recursive systematic 4-state convolutional code with Max-Log-maximum a posteriori probability (MAP) decoding is presented. The results show that recursive systematic convolutional codes give better performance than non-systematic convolutional codes for very noisy channel.

In this correspondence, an analytical technique for bit-error probability of 2-state convolutional code with Max-Log-maximum a posteriori probability (MAP) decoding is presented. This technique employs an iterative calculation of the probability density function (pdf) of the state metric per one transition, and gives the exact the bit-error probability for the overall signal-to-noise ratio (SNR)

First, the calculation method of weight distribution of terminated convolutional codes is shown. Next, it is shown that generalized weight distribution can be obtained since the constraint length is two or three. Furthermore, some results of terminated convolutional codes are shown as function of the number of information symbols.

Two-dimensional (2-D)/three-dimensional (3-D) registration techniques using single-plane fluoroscopy are highly important for analyzing 3-D kinematics in applications such as total knee arthroplasty (TKA) implants. The accuracy of single-plane fluoroscopy-based techniques in the determination of translation perpendicular to the image plane (depth position), however, is relatively poor because a change in the depth position causes only small changes in the 2-D silhouette. Accuracies achieved in depth position using conventional 2-D/3-D registration techniques are insufficient for clinical applications. Therefore, we propose a technique for improving the accuracy of depth position determination in order to develop a system for analyzing knee kinematics over the full six degrees of freedom (6 DOF) using single-plane fluoroscopy. In preliminary experiments, the behaviors of errors for each free variable were quantified as evaluation curves by examining changes in cost function with variations in the free variable. The evaluation curve for depth position was more jagged, and the curve peak less pointy, compared to the evaluation curves of the other five variables, and the curve was found to behave differently. Depth position is therefore optimized independently of the other variables, using an approximate evaluation curve of depth position prepared after initial registration. Accuracy of the proposed technique was evaluated by computer simulation and in vitro tests, with validation of absolute position and orientation performed for each knee component. In computer simulation tests, root-mean-square error (RMSE) in depth position was improved from 2.6 mm (conventional) to 0.9 mm (proposed), whereas for in vitro tests, RMSE improved from 3.2 mm to 1.4 mm. Accuracy of the estimation of the remaining two translational and three rotational variables was found to be almost the same as that obtained by conventional techniques. Results of in vivo tests are also described in which the possibility of full 6 DOF kinematic analysis of TKA implants is shown.

In this paper, the exact analysis of bit error probability of 2- and 4-state Viterbi decoding over binary symmetric channels are demonstrated. It is shown that the results are effective for low signal-to-noise power ratio where bounds are useless. Furthermore, the extension to 2-state soft decision decoding is investigated.

This paper describes several new methods and software for automatic segmentation of the pelvis and the femur, based on clinically obtained multislice computed tomography (CT) data. The hip joint is composed of the acetabulum, cavity of the pelvic bone, and the femoral head. In vivo CT data sets of 60 actual patients were used in the study. The 120 (60 x 2) hip joints in the data sets were divided into four groups according to several key features for segmentation. Conventional techniques for classification of bony tissues were first employed to distinguish the pelvis and the femur from other CT tissue images in the hip joint. Automatic techniques were developed to extract the boundary between the acetabulum and the femoral head. An automatic method was built up to manage the segmentation task according to image intensity of bone tissues, size, center, shape of the femoral heads, and other characters. The processing scheme consisted of the following five steps: 1) preprocessing, including resampling 3-D CT data by a modified Sinc interpolation to create isotropic volume and to avoid Gibbs ringing, and smoothing the resulting images by a 3-D Gaussian filter; 2) detecting bone tissues from CT images by conventional techniques including histogram-based thresholding and binary morphological operations; 3) estimating initial boundary of the femoral head and the joint space between the acetabulum and the femoral head by a new approach utilizing the constraints of the greater trochanter and the shapes of the femoral head; 4) enhancing the joint space by a Hessian filter; and 5) refining the rough boundary obtained in step 3) by a moving disk technique and the filtered images obtained in step 4). The above method was implemented in a Microsoft Windows software package and the resulting software is freely available on the Internet. The feasibility of this method was tested on the data sets of 60 clinical cases (5000 CT images).

Measuring the thickness of sheet-like thin anatomical structures, such as articular cartilage and brain cortex, in three-dimensional (3-D) magnetic resonance (MR) images is an important diagnostic procedure. This paper investigates the fundamental limits on the accuracy of thickness determination in MR images. We defined thickness here as the distance between the two sides of boundaries measured at the subvoxel resolution, which are the zero-crossings of the second directional derivatives combined with Gaussian blurring along the normal directions of the sheet surface. Based on MR imaging and computer postprocessing parameters, characteristics for the accuracy of thickness determination were derived by a theoretical simulation. We especially focused on the effects of voxel anisotropy in MR imaging with variable orientation of sheet-like structure. Improved and stable accuracy features were observed when the standard deviation of Gaussian blurring combined with thickness determination processes was around square root of 2/2 times as large as the pixel size. The relation between voxel anisotropy in MR imaging and the range of sheet normal orientation within which acceptable accuracy is attainable was also clarified, based on the dependences of voxel anisotropy and the sheet normal orientation obtained by numerical simulations. Finally, in vitro experiments were conducted using an acrylic plate phantom and a resected femoral head to validate the results of theoretical simulation. The simulated thickness was demonstrated to be well-correlated with the actual in vitro thickness.

In this paper, we demonstrate an exact analysis of bit probability for trellis coded modulation by using an analytical technique which is effective even in the region of low signal-to-noise power ratio (SNR). This employs an iterative calculation of probability density function (pdf) of path metric per transition, and is applicable for multilevel coded modulation. We show error performance results of 4-ary trellis coded modulation employing 2-state convolutional encoders.