• The Journal of Korean Institute of Communications and Information Sciences
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• v.39A no.4
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• pp.165-171
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• 2014

The rate of the channel code can be controlled by various methods. Puncturing is one of the methods of increasing the code rate, and the original code before puncturing is called the mother code. Any (n,k) convolutional code is obtainable by puncturing some mother codes, and the process of finding the mother code is necessary for designing the optimum channel decoder. In this paper, we proved that any (n,n-1) convolutional code has (2,1) mother codes regardless of the puncturing pattern and showed that they must be equivalent.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.41 no.4
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• pp.379-386
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• 2016

Puncturing is the most common way of increasing the rate of convolutional codes. The puncturing process is done to the original code called the mother code by a specific puncturing pattern. In this article, we investigate into the question whether any convolutional code is obtainable by puncturing some (n, 1) mother codes. We present two sufficient conditions for the mother code and the puncturing pattern to satisfy in order that the punctured code is equivalent to the given (N, K) convolutional code.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.731-736
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• 2017

It is well-known that there exists a constant-weight $[s{\theta}_{k-1},k,sq^{k-1}]_q$ code for any positive integer s, which is an s-fold simplex code, where ${\theta}_j=(q^{j+1}-1)/(q-1)$. This gives an upper bound $n_q(k,sq^{k-1}+d){\leq}s{\theta}_{k-1}+n_q(k,d)$ for any positive integer d, where $n_q(k,d)$ is the minimum length n for which an $[n,k,d]_q$ code exists. We construct a two-weight $[s{\theta}_{k-1}+1,k,sq^{k-1}]_q$ code for $1{\leq}s{\leq}k-3$, which gives a better upper bound $n_q(k,sq^{k-1}+d){\leq}s{\theta}_{k-1}+1+n_q(k-1,d)$ for $1{\leq}d{\leq}q^s$. As another application, we prove that $n_q(5,d)={\sum_{i=0}^{4}}{\lceil}d/q^i{\rceil}$ for $q^4+1{\leq}d{\leq}q^4+q$ for any prime power q.

• Corrosion Science and Technology
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• v.11 no.6
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• pp.225-231
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• 2012

Fitness-for-Service is a useful technology to determine replacement timing, next inspection timing or in-service when nuclear power plant's buried pipes are damaged. If is possible for buried pipes to be aged by material loss, cracks and occlusion as operating time goes by. Therefore Fitness-for-Service technology for buried pipe is useful for plant industry to perform replacement and repair. Fitness-for-Service for buried pipe is studied in terms of existing code and standard for Fitness-for-Service and a current developing code case. Fitness-for-Service for buried pipe was performed according to Code Case N-806 developed by ASME (American Society of Mechanical Engineers).

• Journal of the Korean Society of Safety
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• v.22 no.1 s.79
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• pp.13-18
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• 2007

Structural integrity assessment of thin-walled pipes and pipe items has become one of the major issues in the nuclear power plant. ASME Section XI Code Case N-597-2 provides a criterion for acceptance of the pipes. But the code case has several limitations for application and sometimes gives too conservative or non-conservative results. So it is necessary to understand fully the technical bases of the code case. In the code case N-597, the allowable local thicknesses of thinned straight pipes are given for three different cases. Because of the different technical base, each case gives different thickness values and sometimes gives contradictory values. In this paper attempts were made in order to propose a unified rule for the allowable local thickness and in order to remove or relax the restrictions on the application of the code case. For this purpose elastic stress analyses were made using the finite element method and the stress results were examined. Based on the obtained bending stress results, a very simple procedure was proposed to obtain the consistent allowable local thickness for the thinned straight pipes.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.107-120
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• 2008

There has been a recent growth of interest in codes with respect to a newly defined non-Hamming metric grown as the Rosenbloom-Tsfasman metric (RT, or $\rho$, in short). In this paper, the definitions of the Lee complete $\rho$ weight enumerator and the exact complete $\rho$ weight enumerator of a code over $M_n_\times_s(Z_4)$ are given, and the MacWilliams identities with respect to this RT metric for the two weight enumerators of a linear code over $M_n_\times_s(Z_4)$ are proven too. At last, we also prove that the MacWilliams identities for the Lee and exact complete $\rho$ weight enumerators of a linear code over $M_n_\times_s(Z_4)$ are the generalizations of the MacWilliams identities for the Lee and complete weight enumerators of the corresponding code over $Z_4$.

• ETRI Journal
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• v.34 no.4
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• pp.637-640
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• 2012

The Davey-MacKay construction is a promising concatenated coding scheme involving an outer $2^k$-ary code and an inner code of rate k/n, for insertion-deletion-substitution channels. Recently, a lookup table (LUT)-based inner decoder for this coding scheme was proposed to reduce the computational complexity of the inner decoder, albeit at the expense of a slight degradation in word error rate (WER) performance. In this letter, we show that negligible deterioration in WER performance can be achieved with an LUT as small as $7{\cdot}2^{k+n-1}$, but no smaller, when the probability of receiving less than n-1 or greater than n+1 bits corresponding to one outer code symbol is at least an order of magnitude smaller than the WER when no LUT is used.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.46 no.10
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• pp.14-27
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• 2009

Polar Code was proposed by Turkish professor Erdal Arikan in 2006 as an idea that splitted input channel is increasing the cutoff rate. The channel polarization consisted of code sequences with symmetric high rate capacity in a given B-DMC(Binary-input Discrete Memoryless Channel) W. The symmetric capacity is the highest rate achievable subject to using the input letters of the channel with equal probability. The channel polarization is said to a set of given N independent outputs of B-DMC W. In other word, N increases when N is a set of binary-input channels {$W^{(i)}_N\;:\;1{\leq}\;i\;{\leq}\;N$}, in I{WN(i)} as the fraction of indices is near to 1, which is approaching to I(W), and it is near to 0, then to 1-I(W), where I(W) presents high rates in reliable wireless communication channel as inputs of W with equal frequences. After all, {WN(i)} is shown to be a state of channel coding. On the based on this Polar codes, this paper analyzes Polar coding and decoding of Arikan and propose Radix4 Polar coding newly.

• The Journal of the Korea institute of electronic communication sciences
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• v.18 no.3
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• pp.495-508
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• 2023

This paper proposes a method to find out the type and location information of Pauli X, Y, Z errors generated in quantum channels using only the quantum information processing part of the multiple-rate quantum turbo short-block code without external help from the classical information processing part. In order to obtain the location information of the Pauli X,Y error, n-auxiliary qubits and n-CNOT gates were inserted into the C[n,k,2] QSBC-QURC encoder. As a result, the maximum coding rate is limited to about 1/2 as the trade-off characteristics. The location information of the Pauli Z error for C[n,k,2] QSBC-QURC was obtained through the Clifford-based stabilizer measurement. The proposed method inherits all other characteristics of C[n,k,2] QSBC-QURC except for the coding rate.

• Journal of electromagnetic engineering and science
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• v.7 no.1
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• pp.17-27
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• 2007

Jacket matrices which are defined to be $n{\times}n$ matrices $A=(a_{jk})$ over a field F with the property $AA^+=nI_n$ where $A^+$ is the transpose matrix of elements inverse of A,i.e., $A^+=(a_{kj}^-)$, was introduced by Lee in 1984 and are used for signal processing and coding theory, which generalized the Hadamard matrices and Center Weighted Hadamard matrices. In this paper, some properties and constructions of Jacket matrices are extensively investigated and small orders of Jacket matrices are characterized, also present the full rate and the 1/2 code rate complex orthogonal space time code with full diversity.