• Journal of Information Processing Systems
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• v.10 no.1
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• pp.69-80
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• 2014

The free distance of (n, k, l) convolutional codes has some connection with the memory length, which depends on not only l but also on k. To efficiently obtain a large memory length, we have constructed a new class of (2k, k, l) convolutional codes by (2k, k) block codes and (2, 1, l) convolutional codes, and its encoder and generation function are also given in this paper. With the help of some matrix modules, we designed a single structure Viterbi decoder with a parallel capability, obtained a unified and efficient decoding model for (2k, k, l) convolutional codes, and then give a description of the decoding process in detail. By observing the survivor path memory in a matrix viewer, and testing the role of the max module, we implemented a simulation with (2k, k, l) convolutional codes. The results show that many of them are better than conventional (2, 1, l) convolutional codes.

• Smart Media Journal
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• v.2 no.2
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• pp.39-43
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• 2013

In this paper, we suggest a new technique for WPC parity-check matrix (H-matrix) generation and a corresponding decoding process. The key idea is to construct WPC H-matrix by using a convolutional encoder. It is easy to have many different coderates from a mother code with convolutional codes. However, it is difficult to have many different coderates with LDPC codes. Constructing LDPC Hmatrix based on a convolutional code can easily bring the advantage of convolutional codes to have different coderates. Moreover, both LDPC and convolutional decoding algorithms can be applied altogether in the decoding part. This process prevents the performance degradation of short-length WPC code.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.14 no.4
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• pp.374-387
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• 1989

The decoding method of Binary BCH Codes using symmetric matrix is proposed in this paper. With this method, the error-locator-polynomial is composed by symmetric matrix which consists of the powers of the unknown X plus the synfromes as its elements. The symmetric matirx can also be represented in terms of the unknown X. But the each coefficients of the error-locator polynomial represents the matirx with the syndromes as its entries. By utilizing this proposed algorithm, the device for decoding circuit of the (63, 45) BCH Code for t=3 has been implemented for demonstration.

• Journal of the Korea Convergence Society
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• v.4 no.3
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• pp.27-33
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• 2013

Conventional bar code has the appearance of line bars and spaces, called as one-dimensional bar code. In contrast, the information in two-dimensional bar code is represented by either a small, rectangular or square with the types of mosaic and Braille. The two-dimensional bar code is much more efficient than one-dimensional bar code because it can allow to store and express large amounts of data in a small space and so far there is also a little information about decoding the Data Matrix in base 256 mode. According to the ISO international standards, there are four kinds of bar code: QR code, Data Matrix, PDF417, and Maxi code. In this paper, among them, we focus on describing the basic concepts of Data Matrix in base 256 mode, how to encode and decode them, and how to organize them in detail. In addition, Data Matrix can be organized efficiently depending on the modes of numeric, alphanumeric characters, and binary system and expecially, we focus on describing how to decode the Data Matrix code by four modes.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.1
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• pp.47-52
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• 2002

In this paper we propose a simple decoding algorithm for the 4-ary lexicographic codes (or lexicodes) of length 10 with minimum distance 4, write $S_{10,4}$. It is based on the syndrome decoding method. That is, using a syndrome vector we detect an error and it will be corrected an error from the four parity check equations.

• Communications of Mathematical Education
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• v.6
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• pp.371-381
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• 1997

Let p be an odd prime number. We introduce simple and useful decoding algorithm for orthogonal Latin square codes of order p. Let H be the parity check matrix of orthogonal Latin square code. For any x ${\in}$ GF(p)$^{n}$, we call xH$^{T}$ the syndrome of x. This method is based on the syndrome decoding for linear codes. In L$_{p}$, we need to find the first and the second coordinates of codeword in order to correct the errored received vector.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.1
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• pp.227-247
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• 2018

For intermittently connected wireless sensor networks deployed in hash environments, sensor nodes may fail due to internal or external reasons at any time. In the process of data collection and recovery, we need to speed up as much as possible so that all the sensory data can be restored by accessing as few survivors as possible. In this paper a novel redundant data storage algorithm based on minimum spanning tree and quasi-randomized matrix-QRNCDS is proposed. QRNCDS disseminates k source data packets to n sensor nodes in the network (n>k) according to the minimum spanning tree traversal mechanism. Every node stores only one encoded data packet in its storage which is the XOR result of the received source data packets in accordance with the quasi-randomized matrix theory. The algorithm adopts the minimum spanning tree traversal rule to reduce the complexity of the traversal message of the source packets. In order to solve the problem that some source packets cannot be restored if the random matrix is not full column rank, the semi-randomized network coding method is used in QRNCDS. Each source node only needs to store its own source data packet, and the storage nodes choose to receive or not. In the decoding phase, Gaussian Elimination and Belief Propagation are combined to improve the probability and efficiency of data decoding. As a result, part of the source data can be recovered in the case of semi-random matrix without full column rank. The simulation results show that QRNCDS has lower energy consumption, higher data collection efficiency, higher decoding efficiency, smaller data storage redundancy and larger network fault tolerance.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.49 no.7
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• pp.48-55
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• 2012

Because of increasing complexity in maximum-likelihood (ML) decoding of four of higher antenna scenario, Partial Interference Cancellation (PIC) group decoding could be the perfect solution to reduce the decoding complexity occurs in ML decoding. In this paper, we separate the symbols the users in the layered basis and find the equivalent channel matrix. Based on the equivalent channel matrix we provide the grouping scheme. In our paper, we construct a block wise transmission technique which will achieve the desired code rate and reduce the complexity and provide less transmission time. Finally we show the different grouping performance.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.47 no.5
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• pp.18-24
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• 2010

In this paper, a new matrix decoding system using vector based Virtual Source Location Information (VSLI) is proposed as an alternative to the conventional Dolby Pro logic II/IIx system for reconstructing multi-channel output signals from matrix encoded two channel signals, Lt/Rt. This new matrix decoding system is composed of passive decoding part and active part. The passive part makes crude multi-channel signals using linear combination of the two encoded signals(Lt/Rt) and the active part enhances each channel regarding to the virtual source which is emergent in each inter channel. Since the virtual sources are related to the perceptual sound images in virtual sound field, the reconstructed multi-channel sound results in good dynamic perception and stable image localization. Moreover, the good channel separation is maintained with nonlinear trigonometric enhancing function.

• Journal of Communications and Networks
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• v.10 no.1
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• pp.5-9
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• 2008

Researchers have investigated many upper bound techniques applicable to error probabilities on the maximum likelihood (ML) decoding performance of turbo-like codes and low density parity check (LDPC) codes in recent years for a long codeword block size. This is because it is trivial for a short codeword block size. Previous research efforts, such as the simple bound technique [20] recently proposed, developed upper bounds for LDPC codes and turbo-like codes using ensemble codes or the uniformly interleaved assumption. This assumption bounds the performance averaged over all ensemble codes or all interleavers. Another previous research effort [21] obtained the upper bound of turbo-like code with a particular interleaver using a truncated union bound which requires information of the minimum Hamming distance and the number of codewords with the minimum Hamming distance. However, it gives the reliable bound only in the region of the error floor where the minimum Hamming distance is dominant, i.e., in the region of high signal-to-noise ratios. Therefore, currently an upper bound on ML decoding performance for turbo-like code with a particular interleaver and LDPC code with a particular parity check matrix cannot be calculated because of heavy complexity so that only average bounds for ensemble codes can be obtained using a uniform interleaver assumption. In this paper, we propose a new bound technique on ML decoding performance for turbo-like code with a particular interleaver and LDPC code with a particular parity check matrix using ML estimated weight distributions and we also show that the practical iterative decoding performance is approximately suboptimal in ML sense because the simulation performance of iterative decoding is worse than the proposed upper bound and no wonder, even worse than ML decoding performance. In order to show this point, we compare the simulation results with the proposed upper bound and previous bounds. The proposed bound technique is based on the simple bound with an approximate weight distribution including several exact smallest distance terms, not with the ensemble distribution or the uniform interleaver assumption. This technique also shows a tighter upper bound than any other previous bound techniques for turbo-like code with a particular interleaver and LDPC code with a particular parity check matrix.