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In this paper we discuss a method for reducing the error propagation based on a combination of the error correcting code and the runlength limited code. When the runlength limited code and the error correcting code are used together, the runlength limited encoding is usually applied after the data have been encoded by the encoder of the error correcting code. However, error propagation generated in the data transmission channel can be substantially mitigated during the decoding of the runlength limited code if the runlength encoding is implemented first with subsequent implementation of the error correcting code. The method proposed in this paper consists of a periodic insertion of check symbols in the data sequence encoded first by the runlength limited code and then by the error correcting code. We also proposed a new runlength limited code suitable for the proposed combined method and evaluated its performance. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(11): 45–51, 2001 [ABSTRACT FROM AUTHOR]

Slepian and Wolf considered a coding system (called SW system) for coding the multiterminal (information) source. This paper extends the SW system and defines anew a system (called SWL system) where encoders are mutually links. The problem of determining the optimal error exponent in the admissible rate region has not been answered completely for the SW system. It is shown in this paper that this problem can completely be solved for the SWL system. It is shown also that the optimal exponent can be achieved by the universal code. It is shown further that even if the encoders are linked, the admissible rate region is not enlarged and the reliability of the information transmission is not improved when the transmission rate is outside the admissible rate region. It is interesting to note that those results correspond in a sense to those for the channel with feedback. [ABSTRACT FROM AUTHOR]

The error-control code is used widely at present in digital communication and storage systems. When the error-control code is applied to the actual system, however, several problems arise that cannot be solved by the traditional code theory. One such problem is synchronization. In the usual application of the error-control code, it is not tacitly assumed that the synchronization is already established. Such an assumption is not always valid in the actual situation. If the synchronization is not established, it is difficult for the error-control code to exhibit its full error correction ability. From such a viewpoint, this paper does not use the assumption that the synchronization is established. Both the initial synchronization and error control are considered, i.e., the establishment of synchronization from the unsynchronized state and the execution of the correct decoding are discussed. This paper proposes the initial synchronization decoding model. Two code structures are considered, and the decoding method as well as the asymptotic properties of the error exponent are discussed. As a result, a practical theory for the synchronization and error control is shown, considering simultaneously the initial synchronization and error control. Its features are the high efficiency and the decoding which is not very complex. [ABSTRACT FROM AUTHOR]

When multivalued images are transformed to binary images, the error diffusion method is often used because it is excellent in gray scale representation. When the error diffusion method is applied by means of a raster scan, equal-color regions with all black pixels or all white pixels occur along the edges. This phenomenon has the effect of emphasizing the edges, and the edges may be visually emphasized excessively. In this paper, in order to freely control the equal-color regions, a method that adaptively adjusts the filter coefficients in the error diffusion method based only on the difference from the points to be processed is presented. The filter coefficients are computed by using fuzzy reasoning. According to the proposed method, the width of the equal-color region near a step edge can be controlled adequately by providing appropriate values. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(2): 82–90, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1135 [ABSTRACT FROM AUTHOR]

In this paper, a new decoding algorithm is proposed in which high-dimensional coding is done in a parity check code (high-dimensional ring code). The decoding method for the previously reported ring code has a complex correcting algorithm and requires much calculation time. We have focused on the point that a high-dimensional ring code can be divided into a number of two-dimensional ring codes, and by repeating the error correction of two-dimensional ring codes that requires small computation, we can perform error correction of high-dimensional ring codes. This decoding algorithm has a correction ability similar to the conventional decoding algorithms but with less computation. Moreover, when the error rate is high, random error and burst errors are mixed and an error correcting code is needed. However, since the decoding algorithm of the proposed code has a provision for dimensional division and the error generated on the transmitted block can be uniformly distributed on each two-dimensional plane, the error on the channel in the two-dimensional plane becomes random and error correction can be done efficiently. Moreover, if analysis or simulation increases the number of dimensions, then the correction ability is increased and the limit of the correction ability is determined from the size m of the code. The performance of convolutional codes and Reed Solomon codes is compared and it is shown that the ring code has high processing gain of error correction and that if the threshold point of correction lies in the high-error-rate region, then the decoding error rate is small and this code can be applied to high-error-rate correction. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(5): 75–85, 2001 [ABSTRACT FROM AUTHOR]

In this paper, a generalized version of the Hyperbolic Cascaded Reed–Solomon (HCRS) code proposed by K. Saints and C. Heegard is considered. The lower bound of the minimum distance (the design distance) is investigated. This is a linear code that can be expressed as (n, k, d min = d ) on GF(q). Here, n, k, dmin, and d are the code length, dimension, minimum distance, and design distance, respectively. The proposed code has more degrees of freedom in selection of the code length than the HCRS code. Codes with various code length can be constructed easily. However, in the m-dimensional space on GF(q), the selectable code length is less than qm. When the proposed code with a code length less than qm is compared with the shortened code with the same code length obtained by shortening the m-dimensional HCRS code with a code length of qm [or (q-1)m], the design distances are identical, whereas the proposed code has an equal or greater dimension compared with the HCRS code. Also, from the proposed code, it is relatively easy to construct a code of the same code length as the algebraic geometric code (geometric Goppa code) and the improved geometric Goppa code proposed by Feng and Rao. Further, when the performance (parameters) is compared at a high coding rate (k/n), the proposed code sometimes has equal or better performance. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(11): 18–27, 1999 [ABSTRACT FROM AUTHOR]

In digital VCRs for home use, the video signal for each field is recorded on multiple tracks. Thus, it is difficult to reproduce the video signal smoothly in high-speed trick playback, where the signal is restored by scanning across the tracks. This paper intends to realize a satisfactory high-speed reproduction, and discusses the improvement of the head scanning trajectory, a high-speed trick playback error-control method, and a data coding method for the high-speed trick playback. In the base-band recording VCR, there is a problem that the fixed position of the image frame cannot be restored in integer-multiple speed playback. In order to cope with this problem, a method to adjust the drum rotation speed is considered, and the relation between the variation of the drum rotation and the period of the image presentation is derived. In the high-speed playback, only the C1 code can be restored among the error-correcting codes. For this problem, it is shown that the C3 code can be added and the error-correcting capability can be improved when a data area for high-speed trick playback is provided as in the bit-stream recording VCR. The requantization coding and the data-division coding methods are proposed as data coding methods for the high-speed trick playback. The effectiveness of those methods is demonstrated by image simulation. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(12): 65–81, 1997 [ABSTRACT FROM AUTHOR]

This paper discusses a theoretical method for estimating the error-connecting capability (ECC) of difference-set cyclic codes (DSCC). DSCCs can be decoded by using majority logic decoding (MLD) however, variable threshold decoding (VTD) is often employed to improve performance. A combinational consideration of the ECC using MLD first must define the probability of failure to correct errors at each reference bit. Both the perfect recovery rate and the discrete probability density (DPD) of residual errors after an MLD processing are then calculated. The ECC achieved by using VTD quipped with two concatenated MLDs is estimated based on the DPD. The numerical estimations of the ECC are examined by comparing them with conventional computer simulation results. These results show that the calculated values conform well to the simulation values. The proposed method can be applied efficiently to test both error-correcting chips and the design of the built-in self-test circuit for them. Results can also be applied to estimate the performance of new super-long codes, to which little attention has been paid so far. [ABSTRACT FROM AUTHOR]

The weight distribution of a code usually is investigated on the basis of Hamming weight. For such nonbinary codes as Reed-Solomon (RS) codes, therefore, all nonzero components of codewords are regarded as identical. To describe the structure of nonbinary codes in more detail, each nonzero component should be distinguished from the other. This requirement can be met by the complete weight distribution (CWD). Recently, Blake and Kith and the present authors derived independently the CWD for a special class of RS codes. However, the derivation of the CWD for general RS codes remains a difficult problem. This paper discusses the problem of obtaining the CWD for general RS codes. To make this process easier, three unique sets of codewords which should be examined are defined first. Then it is shown that the CWD can be derived from such unique sets of codewords. Finally, a relationship between the CWD for RS code of dimension k and that of dimension k + 1 is considered. [ABSTRACT FROM AUTHOR]

The concatenated coding scheme using convolutional coding with Viterbi decoding for inner code and Reed-Solomon (RS) code for outer codes is an attractive scheme that can achieve a coding gain larger than that of the convolutional coding with the Viterbi decoding scheme. Hence, it has attracted attention in a wide range of fields in satellite communications from space communications to digital image transmission systems. This paper presents the configuration and characteristics of a newly developed concatenated coding scheme with variable coding gain. This scheme enables selection of a coding gain considering the signal processing time of coding and decoding by enabling selection of: 1) the block length of the RS code (and its error-correction capability); 2) the depth of interweaving combining the inner and outer code by a single codec. In addition, in this scheme, a new synchronization word detection method was developed and employed. In this method, nonlinear conversion is applied to soft decision demodulated data to .synchronize the RS codeword and interleaving, it has been confirmed by numerical calculations that this synchronization word detection method has characteristics further improved over those of the conventional soft decision synchronization word detection method which is superior to the hard decision method. An experimental system was developed and the field test via Ka-band satellite of communication satellite No. 3 (CS-3) was performed, and the tradeoff relationships between the coding/decoding signal processing time and coding gain have been clarified quantitatively. [ABSTRACT FROM AUTHOR]

The structural units in multivalued (MV) information processing systems, such as the MV Arithmetic unit which executes arithmetic operations, the MV memory unit in which MV information is stored, and the MV sequential unit which contains counters, have been widely studied and reported on. There have been very few studies, however, on the encoder and decoder necessary to transmit and store the data in an MV system. In this paper, we present the most primitive ternary codes used in MV error detecting/correcting codes with parallel input signals. Ternary codes ate useful for improving the reliability of an MV information processing system. First, examples of ternary three-digit codes coded in ternary coded decimal (TCD) are shown and their characteristics described. Then we describe single-error correcting ternary Hamming code I code I′, code I″, and code II, from extensions of the binary Hamming codes to ternary. As a result, increases in the maximum code length may be realized. Finally, we present the design of an encoder and decoder with a single-error correcting Hamming code II in a parallel input system and discuss the implementation of these circuits. [ABSTRACT FROM AUTHOR]

Error-correcting codes are introduced widely as a technique to improve the reliability of the digital communication system. Let q be a prime power. The error-correcting codes over CF (q) can be used to correct or detect errors in a (q - 1)-adic numbers system, when only those codewords not having a specific element of CF (q) as the components are utilized. However, the problem concerning the number of code words that do not have a specific nonzero element as the component, has not been answered. Neither has there been a study on this problem. This paper introduces a new concept of the nonzero-element distribution for the codes over GF (q). This distribution indicates how a specific nonzero element of GF (q) distributes among the components of the codewords. Then the maximum distance separable codes over GF (q) is considered, and their nonzero-element distributions are discussed. As a result, a recurrence formula is derived which is useful in determining the nonzero-element distribution of the maximum distance separable codes. For several classes of Reed-Solomon codes, which are the very important members of the maximum distance separable codes, the formulae are derived which specify the nonzero-element distributions. [ABSTRACT FROM AUTHOR]

The arithmetic AN codes are useful fur error detection or error correction in both arithmetic operation and digital data transmission. Especially, the cyclic AN codes based on an even-radix number system are considered to be practical. This paper presents a fundamental theory of quaternary arithmetic distance and symmetric quaternary number system using five numerals, -2, -1, 0, 1, 2. Following an introduction of the cyclic AN codes, we describe a modular number system and some important properties of Lee-type modular arithmetic distance. An elementary method to calculate the minimum distance of the codes is also provided. [ABSTRACT FROM AUTHOR]