Let U denote a set comprising elements called "keys." The goal of the nearest point problem is to search quickly for a key among some keys x₁ , x_n that is the nearest to a reference key x under a partial order relation defined as (x, y) (x, z) for x, y, zU if d(x, y)d(x, z) given a wide-sense distance measure d. This article proposes a method of rearranging x₁ , x_n into a binary perfectly-balanced tree for solving quickly the nearest point problems. Further, computational performances of the proposed method are evaluated experimentally.

Redundancy is introduced by sampling a bandlimited signal at a higher rate than the Nyquist rate. In the cases of erasures due to fading or jamming, the samples are discarded. Therefore, what we get at the output of the receiver is a set if nonuniform samples obtained from a uniform sampling process with missing samples. As long as the rate of nonuniform samples is higher than the Nyquist rate, the original signal can be recovered with no errors. The sampling theorem can be shown to be equivalent to the fundamental theorem of information theory. This oversampling technique is also equivalent to a convolutional code of infinite constraint length is the Field of real numbers. A DSP implementation of this technique is through the use of a Discrete Fourier Transform (DFT), which happens to be equivalent to block codes in the field of real numbers. An iterative decoder has been proposed for erasure and impulsive noise, which also works with moderate amount of additive random noise. The iterative method is very simple and efficient consisting of modules of Fast Fourier Transforms (FFT) and Inverse FFT's. We also suggest a non-linear iterative method which converges faster than the successive approximation. This iterative decoder can be implemented in a feedback configuration. Besides FFT, other discrete transforms such as Discrete Cosine Transform, Discrete Sine Transform, Discrete Hartley Transform, and Discrete Wavelet Transform are used. The results are comparable to FFT with the advantage of working in the field of real numbers.

Most of actual environmental systems show a complicated fluctuation pattern of non-Gaussian type, owing to various kinds of factors. In the actual measurement, the fluctuation of random signal is usually contaminated by an external noise. Furthermore, it is very often that the reliable observation value can be obtained only within a definite fluctuating amplitude domain, because many of measuring equipments have their proper dynamic range and original random wave form is unreliable at the end of amplitude fluctuation. It becomes very important to establish a new signal detection method applicable to such an actual situation. This paper newly describes a dynamical state estimation algorithm for a successive observation contaminated by the external noise of an arbitrary distribution type, when the observation value is measured through a finite dynamic range of measurement. On the basis of the Bayes' theorem, this method is derived in the form of a wide sense digital filter, which is applicable to the non-Gaussian properties of the fluctuations, the actual observation in a finite amplitude domain and the existence of external noise. Differing from the well-known Kalman's filter and its improvement, the proposed state estimation method is newly derived especially by paying our attention to the statistical information on the observation value behind the saturation function instead of that on the resultant noisy observation. Finally, the proposed method is experimentally confirmed too by applying it to the actual problem for a reverberation time measurement from saturated noisy observations in room acoustics.

This paper characterizes a class of optimal fixed-to-fixed length data compression codes for memoryless Gaussian sources that achieve asymptotically the rate-distortion bound under squared-error criterion. Any source output of blocklength n is encoded by two steps, i.e., 1) to quantize in gain by scholar quantizers and 2) to quantize in shape by pointsets on n-dimensional hyperspheres. To show the asymptotic optimality of the proposed codes, rate-distortion properties of the codes are analyzed in detail by using a random coding argument on the n-dimensional unit hypersphere. It is shown that asymptotic behaviors of the proposed codes are mainly determined by the choice of scalar quantizer of the gain. As a results, deep insights into not only the class of asymptotically optimal codes but also the rate-distortion bound itself are obtained.

A linear block code has a finite-length trellis diagram which terminates at the length of the code. Such a trellis diagram is expressed and constructed in terms of sections. The complexity of an L-section trellis diagram for a linear block code is measured by the state and branch complexities, the state connectivity, and the parallel structure. The state complexity is defined as the number of states at the end of each section of the L-section trellis diagram, the branch complexity is defined as the number of parallel branches between two adjacent states, the state connectivity is defined in terms of the number of states which are adjacent to and from a given state and the connections between disjoint subsets of states, and the parallel structure is expressed in terms of the number of parallel sub-trellis diagrams without cross connections between them. This paper investigates the branch complexity, the state connectivity, and the parallel structure of an L-section minimal trellis diagram for a binary linear block code. First these complexities and structure are expressed in terms of the dimensions of specific subcodes of the given code. Then, the complexities of 2ⁱ-section minimal trellis diagrams for Reed-Muller codes are given.

A new Viterbi algorithm with adaptive path reduction method is presented. The proposed system consists of the pre-decoder and reduced path Virerbi decoder. The predecoder separates the mixed channel noise from the received sequence. The number of errors in the pre-decoded error sequence is counted and the path reduction is implemented by the number of errors in pre-decoded error sequence. The path reduction is implemented as a function of channel condition because the errors in the pre-decoded error sequence can be considered as the channel error sequence. Due to the reduction of the path, the number of ACS (add compare select) operations can be reduced, which occupies the dominant part in Viterbi decoding. The ACS reduction ratio for the proposed system achieves up to 30% for the case of (2, 1, 2) Ungerboeck code without degradation of the error performance.

This paper presents two new maximum likelihood decoding (MLD) algorithms for linear codes over Z-channel, which are much more efficient than conventional exhaustive algorithms for high rate codes. In the proposed algorithms, their complexities are reduced by employing the projecting set C_s of the code, which is determined by the "projecting" structure of the code. Space and computational complexities of algorithms mainly depend upon the size of C_s which is usually several times smaller than the total number of codewords. It is shown that the upper bounds on computational complexities of decoding algorithms are in proportion to the number of parity bits and the distance between an initial estimate of the codeword and the received word, respectively, while space complexities of them are equal to the size of C_s. Lastly, numerical examples clarify the average computational complexities of the proposed algorithms, and the efficiency of these algorithms for high rate codes is confirmed.

Asymptotic bounds are considered for unidirectional byte error-correcting codes. Upper bounds are developed from the concepts of the Singleton, Plotkin, and Hamming bounds. Lower bounds are also derived from a combination of the generalized concatenated code construction and the Varshamov-Gilbert bound. As the result, we find that there exist codes of low rate better than those on the basis of Hamming distance with respect to unidirectional byte error-correction.

This paper proposes new design methods for single b-bit (b2) byte error correcting and double bit error detecting code, called SbEC-DED code, suitable for high-speed memory systems using byte organized RAM chips. This new type of byte error control code is practical from the viewpoint of having less redundancy and stronger error control capability than the existing ones. A code design method using elements from a coset of subfield under addition gives the practical SbEC-DED code with 64 information bits and 4-bit byte length which has the same check-bit length, 12 bits, as that of the Hamming single byte error correcting code. This also has very high error detection capabilities of random double byte errors and of random triple bit errors.

A coherent communication system using squeezed light is one of candidates for a realization of super-reliable systems. In order to design such a system, it is essential to understand and to analyze modulators mathematically. However, quantum noise of squeezed light has a colored spectrum which changes with respect to phase of a local laser. Therefore the optimization of the relationship between signal and quantum noise spectrums is required at a modulator to obtain the ultimate performance of the communication system. In this paper, some ideas of modulators for squeezed light are proposed and their spectrum transformations are given. After the brief summary of squeezed quantum noise, a new concept which originates from the restriction of the local laser phase is applied to it. This concept makes a problem originated from a colored quantum noise spectrum more serious. It results in the optimization problem for the relationship between the quantum noise spectrum and signal power spectrum. The solution of this problem is also given under the restriction of local laser phase. As a result, a general design theory for coherent communication system using the squeezed light is given.

A new method by which images are coded with predictable and controllable subjective picture quality in the minimum cost of bit rate is developed. By using wavelet transform, the original image is decomposed into a set of subimages with different frequency channels and resolutions. By utilizing human contrast sensitivity, each decomposed subimage is treated according to its contribution to the total visual quality and to the bit rate. A relationship between physical errors (mainly quantization errors) incurred in the orthonormal wavelet image coding system and the subjective picture quality quantified as the mean opinion score (MOS) is established. Instred of using the traditional optimum bit allocation scheme which minimizes a distortion cost function under the constraint of a given bit rate, we develop an "optimum visually weighted noise power allocation" (OVNA) scheme which emphasizes the satisfying of a desired subjective picture quality in the minumum cost of bit rate. The proposed method enables us to predict and control the picture quality before the reconstruction and to compress images with desired subjective picture quality in the minimum bit rate.

This paper first proposes a fast fingerprint identification method based on a weighted-mean of binary image, and further investigates optimization of the weights. The proposed method uses less computer memory than the conventional pattern matching method, and takes less computation time than both the feature extraction method and the pattern matching method. It is particularly effective on the fingerprints with a small angle of inclination. In order to improve the identification precision of the proposed basic method, three schemes of modifying the proposed basic method are also proposed. The performance of the proposed basic method and its modified schemes is evaluated by theoretical analysis and computer experiment using the fingerprint images recorded from a fingerprint read-in device. The numerical results showed that the proposed method using the modified schemes can improve both the true acceptance rate and the false rejection rate with less memory and complexity in comparison with the conventional pattern matching method and the feature extraction method.

The value distribution of the partial autocorrelation of periodic sequences is important for the evaluation of the sequence performances when sequences of long period are used. But it is difficult to find the exact value distribution of the autocorrelation in general. Therefore we derived some properties of the partial autocorrelation for binary m-sequences which may be used to find the exact value distribution.

In this study, an expression of the regression relationship with less information loss is concretely derived in the form suitable to the existence of amplitude constraint of the observed data and the prediction of response probability distribution. The effectiveness of the proposed method is confirmed experimentally by applying it to the actual acoustic data.

This paper considers the problem of finding a largest common subgraph of graphs, which is an important problem in chemical synthesis. It is known that the problem is NP-hard even if graphs are restricted to planar graphs of vertex degree at most three. By the way, a graph is called an almost tree if E(B)V(B)+ K holds for every block B where K is a constant. In this paper, a polynomial time algorithm for finding a largest common subgraph of two graphs which are connected, almost trees and of bounded vertex degree. The algorithm is an extension of a subtree isomorphism algorithm which is based on dynamic programming. Moreover, it is shown that the degree bound is essential. That is, the problem of finding a largest common subgraph of two connected almost trees is proved to be NP-hard for any K0 if degree is not bounded. The three dimensional matching problem, a well known NP-complete problem, is reduced to the problem.

In this paper, a construction of de Bruijn sequences using maximum length linear sequences is considered. The construction is based on the well-known cross-join (CJ) method: Maximum length linear sequences are used to produce de Bruijn sequences by the CJ process. Properties of the CJ paris in the maximum length linear sequences are investigated. It is conjectured that the number of CJ pairs in a maximum length linear sequence is given by (2^2n-3+1)/3-2^n-2, where n2 is the length of the linear feedback shift register with the sequence. The CJ paris for some special cases are obtained. An algorithm for finding CJ pairs is described and a method of implementation is discussed briefly.

A complete analysis for the quantization noises and the reconstruction noises of the wavelet pyramid coding system is given. It is shown that in the (orthonormal) wavelet image coding system, there exists a simple and exact formula to compute the reconstruction mean-square-error (MSE) for any kind of quantization errors. Based on the noise analysis, an optimal bit allocation scheme which minimizes the system reconstruction distortion at a given rate is developed. The reconstruction distortion of a wavelet pyramid system is proved to be directly proportional to 2^-2, where is a given bit rate. It is shown that, when the optimal bit allocation scheme is adopted, the reconstruction noises can be approximated to white noises. Particularly, it is shown that with only one known quantization MSE of a wavelet decomposition at any layer of the wavelet pyramid, all of the reconstruction MSE's and the quantization MSE's of the coding system can be easily calculated. When uniform quantizers are used, it is shown that at two successive layers of the wavelet pyramid, the optimal quantization step size is a half of its predecessor, which coincides with the resolution version of the wavelet pyramid decomposition. A comparison between wavelet-based image coding and some well-known traditional image coding methods is made by simulations, and the reasons why the wavelet-based image coding is superior to the traditional image coding are explained.

Recently, the small set of nonbinary Kasami sequences was presented and their correlation properties were clarified by Liu and Komo. The family of nonbinary Kasami sequences has the same periodic maximum nontrivial correlation as the family of Kumar-Moreno sequences, but smaller family size. In this paper, first it is shown that each of the nonbinary Kasami sequences is unbalanced. Secondly, a new family of nonbinary sequences obtained from modified Kasami sequences is proposed, and it is shown that the new family has the same maximum nontrivial correlation as the family of nonbinary Kasami sequences and consists of the balanced nonbinary sequences.

In this paper, a definitce relation between the TSP's optimal solution and the attracting region in the parameters space of TSP's energy function is discovered. An many attracting region relating to the global optimal solution for TSP is founded. Then a neural network algorithm with the optimized parameters by using Orthogonal Array Table Method is proposed and used to solve the Travelling Salesman Problem (TSP) for 30, 31 and 300 cities and Map-coloring Problem (MCP). These results are very satisfactory.

Acceleration techniques have been incorporated into the generalized method of characteristics (GMC) to perform transient analysis of uniform transmission lines, for the special case when the transmission lines are driven by digital signals. These techinques have been proved to improve the simulation speed to a great extent when the analysis is carried out using iterative waveform relaxation method. It has been identified that the load impedance connected to the transmission line has a bearing on the efficiency of one of these acceleration techniques. Examples of an RLCG line terminated with linear loads as well as nonlinear loads are given to illustrate the advantage of incorporating these acceleration techniques.

We propose a decoding algorithm for the t-EC/AUED code proposed by Böinck and Tiborg. The proposed algorithm also reveals some remarkable properties of the code.

A model for a large network with an unidirectional linear respone (ULR) is proposed in this letter. This deterministic system has powerful computing properties in very close correspondence with earlier stochastic model based on McCulloch-Pitts neurons and graded neuron model based on sigmoid input-output relation. The exclusive OR problems and other digital computation properties of the earlier models also are present in the ULR model. Furthermore, many analog and continuous signal processing can also be performed using the simple ULR neural network. Several examples of the ULR neural networks for analog and continuous signal processing are presented and show extemely promising results in terms of performance, density and potential for analog and continuous signal processing. An algorithm for the ULR neural network is also developed and used to train the ULR network for many digital and analog as well as continuous problems successfully.

A new arithmetic multiple-valued algebra with functional completeness is introduced. The algebra is called Neuro-Algebra for it has very similar formula and architecture to neural networks. Two canonical forms of multiple-valued functions of this Neuro-Algebra are presented. Since the arithmetic operations of the Neuro-Aglebra are basically a weighted-sum and a piecewise linear operations, their implementations are very simple and straightforward. Furthermore, the multiple-valued networks based on the Neuro-Algebra can be trained by the traditional back-propagation learning algorithm directly.

We derive the eigenvalue constraint for a neural network with three degrees of freedom. The result implies that the neural network needs a neuron with variable output function to generate chaos. It is also shown that the neuron with the special characteristics can be constructed by ordinary neurons.

This letter discusses a behavior of solitons in a Josephson junction transmission line which is described by a perturbed sine-Gordon equation. It is shown that a soliton wave leads a quasi-periodic break down route to chaos in a Josephson transmission line. This route show phase locking, quasi-periodic state, chaos and hyper chaos, and these phenomena are examined by using Poincar sections, circle map, rotation number, and so on.