We define the complexity and the distortion-complexity of an individual finite length string from a finite set. Assuming that the string is produced by a stationary ergodic source, we prove that the distortion-complexity per source letter and its expectation approximate arbitrarily close the rate-distortion function of this source as the length of the string grows. Furthermore, we apply this property to construct a universal data compression scheme with distortion.

A method is presented for computing the number of codewords of weight less than or equal to a given integer in a binary block code by using its trellis diagram. The time and space complexities are analyzed. It is also shown that this method is very efficient for the codes which have relatively simple trellis diagram, say some BCH codes. By using this method, the weight distribution of (128,36) extended BCH code is computed efficiently.

Multilevel RLL (Runlength Limited) sequences are analyzed. Their noiseless capacity and lower bounds on the channel capacity in the presence of additive white Gaussian noise are given. Moreover, the analytical power spectra formulae for those sequences which generalize the previously derived one for binary sequences are newly derived. We conclude from the analysis of the power spectra that multilevel RLL sequences are attractive from the point of view that they increase information rate while keeping low DC-content and self-clocking capability of binary RLL sequences.

The byte error locating codes specify the byte location in which errors are occurred without indicating the precise location of erroneous bit positions. This type of codes is considered to be useful for fault isolation and reconfiguration in the fault-tolerant computer systems. In this paper, difference between the code function of error-location and that of error-correction/error-detection is clarified. With using the concepts of unidirectional byte distance, unordered byte number and ordered byte number, the necessary and sufficient conditions of the unidirectional byte error locating codes are demonstrated.

This papter proposes a new type of unidirectional error control codes which indicates the location of unidirectional errors clustered in b-bit length, i.e., unidirectional byte error in b (b2) bits. Single unidirectional b-bit byte error locating codes, called SUbEL codes, are first clarified using necessary and sufficient conditions, and then code construction algorithm is demonstrated. The lower bound on check bit length of the SUbEL codes is derived. Based on this, the proposed codes are shown to be very efficient. Using the code design concept presented for the SUbEL codes, it is demonstrated that generalized unidirectional byte error locating codes are easily constructed.

Recently there has been considerable interest in coded modulation schemes that offer multiple levels of error protection. That is, constructions of (block or convolutional) modulation codes in which signal sequences associated with some message symbols are separated by a squared Euclidean distance that is larger than the minimum squared Euclidean distance (MSED) of the code. In this paper, the trellis structure of linear unequal-error-protection (LUEP) codes is analyzed. First, it is shown that LUEP codes have trellises that can be expressed as a direct product of trellises of subcodes or clouds. This particular trellis structure is a result of the cloud structure of LUEP codes in general. A direct consequence of this property of LUEP codes is that searching for trellises with parallel structure for a block modulation code may be useful not only in analyzing its structure and in simplifying its decoding, but also in determining its UEP capabilities. A basic 3-level 8-PSK block modulation code is analyzed under this new perspective, and shown to offer two levels of error protection. To illustrate the trellis structure of an LUEP code, we analyze a trellis diagram for an extended (64,24) BCH code, which is a two-level LUEP code. Furthermore, we introduce a family of LUEP codes based on the |||-construction, using Reed-Muller (RM) codes as component codes. LUEP codes in this family have the advantage of having a well known trellis structure. Their application in constructing LUEP-QPSK modulation codes is presented, and their error performance over an AWGN channel examined.

An encoder of a trellis coded modulation (TCM) is composed of a linear convolutional encoder followed by a mapper to channel signals. A new condition, under which the performance evaluation of the TCM is possible based on the 2^ν state error state transition diagram, is proposed, where ν is the number of delay elements in the convolutional encoder. There have been proposed three similar methods. This paper points out the restriction of the previous methods, and proposes a new method. The condition, under which the previous method is useful, is called nuiformity, such as, the error weight profile is independent from the encoder state. When uniformity does not hold, we discuss to divide an error state into substates based on the coset decomposition of output vectors of the convolutional encoder. The coset is determined by the vector called coset selector. If the condition defined as equal dividing holds, the subdivided states can be merged and the performance can be evaluated based on the 2^ν state transition diagram, even for the codes without uniformity. When the row rank of the transformation matrix, from the input vector of the encoder to the coset selector vector, is full, the equal dividing condition holds under the assumption of equally probable i.i.d. (independently identically distributed) input sequence. For TCM schemes without uniformity (in the case, previous methods can not be applied), upper bounds of the bit error rate are evaluated by the proposed method and compared with the simulation results. The difference is less than 10% in the range of bet error rate 10^-4.

We present an 8-dimensional trellis-coded 8-PSK with a symbol transition constraint that is similar to that of π/4-shift quadrature phase shift keying (QPSK). This scheme can achieve a coding gain of 1.6 to 2.4 dB at the same rate of π/4-shift QPSK on Gaussian channel, and it has also an immunity against the integer multiples of 90 phase ambiguities. In order to label the constellation of the proposed scheme, a constellation partitioning algorithm is presented. This algorithm, on the basis of set partitioning, can be used to label the signal constellation with no coset structure.

Recently, a lot of research works have been carried out regarding intelligent communication. If the final information sink is assumed as a human being, a communication channel can be used more effectively when encoders/decoders work "intelligently" or take into account of the semantics of information to be sent. We have been studying error-controlling systems based on different importance of segmental information. The system divides the information input into segments to which individual importance can be assigned. The segments are individually encoded by appropriate error-correcting codes (ECCs) which correspond to their importance among codes with different error-correcting capabilities. For the information that difference of the importance is systematically aligned, conventional UEP (unequal error protection) codes can be applied, but we treat the case that alignment of the importance of the information source is not systematically aligned. Since the system uses multiple ECCs with different (n,k,d) parameters, information regarding what length of the next codeword is required for decoding. We propose error controlling schemes using mulriple ECCs; the first scheme and the second scheme use the obvious codelength identifying information. In the second scheme, information bits are sorted so that segments with the same importance can be encoded by an ECC with the same error-correcting capability. The third scheme is a main proposal in this paper and uses Variable Capability Coding scheme (VCC) which uses some ECCs having different error-correcting capabilities and codelengths. A sequence encoded by the VCC is separable into appropriate segments without obvious codelength identifying information when the channel error probability is low. Subsequently, we evaluate these schemes by coderate when (1) error correcting capability (2) codelength identifying capability are the same. One of the feature of VCC is the capability of resuming from propagative errors because errors beyond the codelength identifying capability occur and the proper beginning of the codeword is lost in the decoder. We also evaluate this capability as (3) resynchronizing capability.

This paper proposes and investigates an intelligent error-controlling scheme according to different importance of segmental information. In particular, the scheme is designed for facial images encoded by model-based coding that is a kind of intelligent compression coding. Intelligent communication systems regard the contents of information to be transmitted with extremely high compression and reliability. After highly efficient information compression by model-beaed coding, errors in the compressed information lead to severe semantic errors. The proposed scheme reduces semantic errors of information for the receiver. In this paper, we consider Action Unit (AU) as a segment of model-based coded facial image of human being and define the importance for each AU. According to the importance, an AU is encoded by an appropriated code among codes with different error-correcting capabilities. For encoding with different error controlling codes, we use three kinds of constructions to obtain unequal error protection (UEP) codes in this paper. One of them is the direct sum construction and the others are the proposed constructions which are based on joint and double coding. These UEP codes can have higher coderate than other UEP codes when minimum Hamming distance is small. By using these UEP codes, the proposed intelligent error-controlling scheme can protect information in segment in order to reduce semantic errors over a conventional error-controlling scheme in which information is uniformly protected by an error-correcting code.

Overlapping multi-pulse pulse position modulation (OMPPM) is a modulation scheme having higher capacity and cutoff rate than other conventional modulation schemes when both off-duration between pulses shorter than a laser pulsewidth and resolution better than a laser pulsewidth are realized [1],[2]. In Refs. [1],[2] erasure events of a few chips that can be decoded correctly is defined as an erasure event. This results in lower bounds on the performance of OMPPM in optical-direct-detection channel in quantum limited case. This paper analyzes more exact performance of OMPPM in optical direct-detection channel in quantum limited case when both off-duration between pulses shorter than a laser pulsewidth and resolution better than a laser pulsewidth are realized. First we derive the error probability of OMPPM with considering what chips are detected or erased. Then we derive the capacity and the cutoff rate of OMPPM using the error probability. It is shown that OMPPM outperforms on-off keying (OOK), pulse position modulation (PPM), multi-pulse PPM (MPPM), and overlapping PPM (OPPM) in terms of both capacity and cutoff rate for the same pulsewidth and the same duty cycle. Moreover, it is shown that OMPPM with fewer slots and more pulses per block has better cutoff rate performance when the average received power per slot is somewhat large.

This paper proposes RSA-type cryptosystems over elliptic curves E_n(O, b) and E_n(a, O),where E_n(a, b): y² x³+ax+b (mod n),and n is a product of from-free primes p and q. Although RSA cryptosystem is not secure against a low exponent attack, RSA-type cryptosystems over elliptic curves seems secure against a low multiplier attack. There are the KMOV cryptosystem and the Demytko cryptosystem that were previously proposed as RSA-type cryptosystems over elliptic curves. The KMOV cryptosystem uses form-restricted primes as p q 2(mod 3)or p q 3(mod 4), and encrypts/decrypts a 2log n-bit message over varied elliptic curves by operating values of x and y coordinates. The Demytko cryptosystem, which is an extension of the KMOV cryptosystem, uses form-free primes, and encrypts/decrypts a log n-bit message over fixed elliptic curves by operating only a value of x coordinates. Our cryptosystems, which are other extensions fo the KMOV cryptosystem, encrypt/decrypt a 2log n-bit message over varied elliptic curves by operating values of x and y coordinates. The Demytko cryptosystem and our cryptosystems have higher security than the KMOV cryptosystem because from-free primes hide two-bit information about prime factors. The encryption/decryption speed in one of our cryptosystems is about 1.25 times faster than that in the Demytko cryptosystem.

Broadcasting with secrecy of messages is important in a situation such as pay television. In pay television only a broadcasting station broadcasts a message. On the other hand, broadcast communication is also important. Broadcast communication means any user in a whole group can broadcast a message to any subset of the group. In this paper the efficiency of secure broadcast communication is discussed in terms of the length of messages sent and the encryption speed. We prove that the length of the broadcast messages is not kept less than O(n), where n is the number of receivers, when a broadcast system has a form of a single system which is defined as the generalized form of an individual key method and a master key method. In contrast, the proposed secure broadcast communication method, a multi-dimension method, keeps the length of messages sent O(m^mn), where m is the number of the dimension used in the multi-dimension method. At the same time the encryption speed was reduced from O(n(log(n+C₂)+C₃)) of the master key method to O(^mn(log^mn+C₁)) of the multi-dimension method.

This paper proposes a dynamically randomized version of DES (called RDES) in which a input-dependent swapping S_k(X) is added onto the right half of the input in each round of DES. This new scheme decreases the probability of success in differential cryptanalysis because it decreases the characteristic probability. Each "best" two-round characteristic probability is analyzed for typical schemes of the RDES: (i) RDES-1 with a simple one-level swapping, (ii) RDES-1' with an optimal one-level swapping, (iii) RDES-2 with a simple two-level swapping, and (iv) RDES-2' with an optimal two-level swapping. The main results are as follows. (a) The differential attacks on the 16-round RDES-1' and the 16-round RDES-2 require more computational time than the exhaustive search. (b) A differential attack is substantially inapplicable to the 16-round RDES-2' because more than 2⁶³ chosen plaintext pairs are required. (c) The encryption/decryption speed of the n-round RDES is almost the same as that of the n-round DES.

A stochastic system represented by an input-output model can be described by mainly two different types of state space representation. Corresponding to state space representations innovation models are examined. The relationship between both representations is made clear systematically. An easy transformation between them is presented. Zeros of innovation models are the same as those of an ARMA model which is stochastically equivalent to innovation models, and related to stable eigenvalues of generalized eigenvalue problem of matrix Riccati equation.

In the actual acoustic environment, the stochastic process exhibits various non-Gaussian distribution forms, and there exist potentially various nonlinear correlations in addition to the linear correlation between time series. In this study, a nonlinear ARMA model is proposed, based on the Bayes' theorem, where no artificially pre-established regression function model is assumed between time series, while reflecting hierarchically all of those various correlation informations. The proposed method is applied to the actual data of road traffic noise and its practical usefulness is verified.

A specific signal in most of actual environmental systems fluctuates complicatedly in a non-Gaussian distribution form, owing to various kinds of factors. The nonlinearity of the system makes it more difficult to evaluate the objective system from the viewpoint of internal physical mechanism. Furthermore, it is very often that the reliable observation value can be obtained only within a definite domain of fluctuating amplitude, because many of measuring equipment have their proper dynamic range and the original random wave form is unreliable at the end of amplitude fluctuation. It becomes very important to establish a new signal processing or an evaluation method applicable to such an actually complicated system even from a functional viewpoint. This paper describes a new trial for the signal processing along the same line of the extended regression analysis based on the Bayes' theorem. This method enables us to estimate the response probability property of a complicated system in an actual situation, when observation values of the output response are saturated due to the dynamic range of measuring equipment. This method utilizes the series expansion form of the Bayes' theorem, which is applicable to the non-Gaussian property of the fluctuations and various kinds of correlation information between the input and output fluctuations. The proposed method is newly derived especially by paying our attention to the statistical information of the input-output data without the saturation operation instead of that on the resultantly saturated observation, differing from the well-known regression analysis and its improvement. Then, the output probability distribution for another kind of input is predicted by using the estimated regression relationship. Finally, the effectiveness of the proposed method is experimentally confirmed too by applying it to the actual data observed for indoor and outdoor sound environments.

In computer vision, the interpretation of 3D motion of an object in the physical world is an important task. This study proposes a 3D motion interpretation method which uses a neural network system consisting of three kinds of neural networks. This system estimates the solutions of 3D motion of an object by interpreting three optical flow (OF-motion vector field calculated from images) patterns obtained at the different view points for the same object. In the system, OF normalization network is used to normalize diverse OF patterns into the normalized OF format. Then 2D motion interpretation network is used to interpret the normalized OF pattern and to obtain the object's projected motion onto an image plane. Finally, 3D motion interpretation network totally interprets the three sets of the projected motions and it derives the solutions of the object's 3D motion from the inputs. A complex numbered version of the back-propagation (Complex-BP) algorithm is applied to OF normalization netwerk and to 2D motion interpretation network, so that these networks can learn graphical patterns as complex numbers. Also a 3D vector version of the back-propagation (3DV-BP) algorithm is applied to 3D motion interpretation network so that the network can learn the spatial relationship between the object's 3D motion and the corresponding three OF patterns. Though the interpretation system is trained for only basic 3D motions consisting of a single motion component, the system can interpret unknown multiple 3D motions consisting of several motion components. The generalization capacity of the proposed system was confirmed using diverse test patterns. Also the robustness of the system to noise was probed experimentally. The experimental results showed that this method has suitable features for applying to real images.

This article shows construction of an asymptotically optimal source code for transmitting sentences together with truth values on a [0,1]-valued logic system.

A uniquely decodable (UD) code pair (C, S) is considered for the two-user binary adder channel. For a class of linear codes C, the maximum independent set of the graph associated with C, which is the second code S, is evaluated. When the rate R₁ of C is less than 0.5, there exist UD codes (C, S)'s such that the rate R₂ of S exceeds the Khachatrian's and Guo's results in amount.

In this paper, trellis coded modulation with bandwidth expansion is examined. The proposed scheme is a modified Symbol-rate-increased TCM [3]-[5], which allows the bandwidth expansion ratio to be varied to an arbitrary value. The Symbol-rate-increased TCM has been shown to be a particular case of the proposed scheme. Simulation results have clarified that the proposed scheme achieves a significant improvement over an uncoded scheme in an AWGN channel.

We analyze the error probability performance of multi-pulse pulse position modulation (MPPM) in noisy photon counting channel. Moreover we investigate the error perofrmance of convolutional coded MPPM and RS coded MPPM in noisy photon counting channel. We define a distance between symbols as the number of nonoverlapping pulses in one symbol, and by using the distance we analyze the error performance of MPPM in noisy photon counting channel. It is shown that MPPM has better performance than PPM in the error probability performance in noisy photon counting channel. For PPM in noisy photon counting channel, convolutional codes are more effective than RS codes to reduce the average transmitting power. For MPPM in noisy photon counting channel, however, RS codes are shown to be more effective than convolutional codes.

This paper describes highly parallel analog image coding and decoding by cellular neural networks (CNNs). The communication system in which the coder (C-) and decoder (D-) CNNs are embedded consists of a differential transmitter with an internal receiver model in the feedback loop. The C-CNN encodes the image through two cascaded techniques: structural compression and halftoning. The D-CNN decodes the received data through a reconstruction process, which includes a dynamic current distribution, so that the original input to the C-CNN can be recognized. The halftoning serves as a dynamic quantization to convert each pixel to a binary value depending on the neighboring values. We approach halftoning by the minimization of error energy between the original gray image and reconstructed halftone image, and the structural compression from the viewpoints of topological and regularization theories. All dynamics are described by CNN state equations. Both the proposed coding and decoding algorithms use only local image information in a space inveriant manner, therefore errors are distributed evenly and will not introduce the blocking effects found in DCT-based coding methods. In the future, the use of parallel inputs from on-chip photodetectors would allow direct dynamic quantization and compression of image sequences without the use of multiple bit analog-to-digital converters. To validate our theory, a simulation has been performed by using the relaxation method on an 150 frame image sequence. Each input image was 256256 pixels whth 8 bits per pixel. The simulated fixed compression rate, not including the Huffman coding, was about 1/16 with a PSNR of 31[dB]35[dB].

This paper describes a pipelining universal system of discrete time cellular neural networks (DTCNNs). The new relaxation-based algorithm which is called a Pipelining Gauss Seidel (PGS) method is used to solve the CNN state equations in pipelining. In the systolic system of N processor elements {PE_i}, each PE_i performs the convolusional computation (CC) of all cells and the preceding PE_i-1 performs the CC of all cells taking precedence over it by the precedence interval number p. The expected maximum number of PE's for the speeding up is given by n/p where n means the number of cells. For its application, the encoding and decoding process of moving images is simulated.

In this paper, the Pisarenko and the Constrained Yule-Walker (CYW) estimators of a tone frequency are first newly derived from the viewpoint of using directly the autocorrelation coefficients. Then, simulation of these two estimators is carried out in some detail. The simulation results show that compared with the Pisarenko estimator the CYW estimator, which has not been adequately studied, works poorly for low and moderate Signal-to-Noise Ratio (SNR) values. However, in case of high SNR value, it yields very small bias and comparable estimation variance, and thus produces more accurate tone frequency estimates.

A capacitor-error-free SC voltage inverter with zero sensitivity to element-value variations is proposed. By virtue of the capacitor-error-free property, this SC voltage inverter is free from the capacitor mismatch. The performance of this SC voltage inverter has been confirmed from both the simulation and experiment.