• Journal of the Institute of Electronics Engineers of Korea TC
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• v.42 no.8 s.338
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• pp.1-10
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• 2005

In this paper, the explicit low density codes construction from the generalized permutation matrices related to algebra theory is investigated, and we design several Jacket inverse block matrices on the recursive formula and permutation matrices. The results show that the proposed scheme is a simple and fast way to obtain the low density codes, and we also Proved that the structured low density parity check (LDPC) codes, such as the $\pi-rotation$ LDPC codes are the low density Jacket inverse block matrices too.

• Journal of electromagnetic engineering and science
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• v.7 no.1
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• pp.28-34
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• 2007

In this paper, we present a quasi-Jacket block matrices over binary matrices which all are belong to a class of cocyclic matrices is the same as the Hadamard case and are useful in digital signal processing, CDMA, and coded modulation. Based on circular permutation matrix(CPM) cocyclic quasi block low-density matrix is introduced in this paper which is useful in coding theory. Additionally, we show that the fast algorithm of quasi-Jacket block matrix.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.47 no.11
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• pp.36-42
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• 2010

This paper presents a hybrid approach to the construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes based on parallel bundles in Euclidean geometries and circulant permutation matrices. Codes constructed by this method are shown to be regular with large girth and low density. Simulation results show that these codes perform very well with iterative decoding and achieve reasonably large coding gains over uncoded system.

• Proceedings of the KIEE Conference
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• 2007.04a
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• pp.252-254
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• 2007

In this paper, we will introduce an encoding algorithm of LDPC Codes in Direct-Sequence UWB systems. We evaluate the performance of the coded systems in an AWGN channel. This new algorithm is based on the Jacket matrics. Mathematically let A = ($a_{kl}$) be a matnx, if $A^{-1}$ = $(a^{-1}_{kl})^r$,then the matrix A is a Jacket matrix. If the Jacket matrices if Low density, the inverse matrices is also Low density which is very important to the introduced encoding algorithm.

• The Journal of the Korea institute of electronic communication sciences
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• v.9 no.4
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• pp.403-408
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• 2014

In this paper, we consider the encoding scheme of low density codes. In particular, we propose the fast encoding algorithm of the low density codes using circulant permutation matrices, The fast encoding algorithm is similar to the fast Hadamard transform, and the results show that the proposed scheme is a simple and fast encoding algorithm of the low density codes.

• Journal of Communications and Networks
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• v.15 no.1
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• pp.71-76
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• 2013

A new class of quantum low-density parity-check (LDPC) codes whose parity-check matrices are dual-containing matrices constructed based on lines of Euclidean geometries (EGs) is presented. The parity-check matrices of our quantum codes contain one and only one 4-cycle in every two rows and have better distance properties. However, the classical parity-check matrix constructed from EGs does not satisfy the condition of dual-containing. In some parameter conditions, parts of the rows in the matrix maybe have not any nonzero element in common. Notably, we propose four families of fascinating structure according to changes in all the parameters, and the parity-check matrices are adopted to satisfy the requirement of dual-containing. Series of matrix properties are proved. Construction methods of the parity-check matrices with dual-containing property are given. The simulation results show that the quantum LDPC codes constructed by this method perform very well over the depolarizing channel when decoded with iterative decoding based on the sum-product algorithm. Also, the quantum codes constructed in this paper outperform other quantum codes based on EGs.

• ETRI Journal
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• v.27 no.5
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• pp.557-562
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• 2005

Low-density parity-check (LDPC) codes have recently emerged due to their excellent performance. However, the parity check (H) matrices of the previous works are not adequate for hardware implementation of encoders or decoders. This paper proposes a hybrid parity check matrix which is efficient in hardware implementation of both decoders and encoders. The hybrid H-matrices are constructed so that both the semi-random technique and the partly parallel structure can be applied to design encoders and decoders. Using the proposed methods, the implementation of encoders can become practical while keeping the hardware complexity of the partly parallel decoder structures. An encoder and a decoder are designed using Verilog-HDL and are synthesized using a $0.35 {\mu}m$ CMOS standard cell library.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.45 no.7
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• pp.1-8
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• 2008

Low Density Parity Check codes(LDPC) are recently focused on communication systems due to its good performance. The standard of WiBro has also included LDPC codes as a channel coding. The weak point of implementation for LDPC encoder is that conventional binary Matrix Vector Multiplier has many clock cycles which limit throughput. In this paper, we propose semi-parallel architecture by using cyclic shift registers and exclusive-OR without conventional Matrix Vector Multipliers over the standard parity check matrices with Circulant Permutation Matrices(CPM). Furthermore, multi-rate encoder is designed by using proposed architecture. Our encoder with multi-rate for IEEE 802.16e LDPC has lower clock cycles and higher throughput.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.2B
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• pp.325-333
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• 2010

Most communication systems including Wibro use quasi-cyclic LDPC codes composed of circulants. However, it is very difficult to design quasi-cyclic(QC) LDPC codes with optimal degree distribution satisfying conditions on layered decoding and girth due to the restriction of the size of its base matrix. In this paper, we propose a good solution by introducing superposition matrices to QC LDPC codes. We derive the conditions on checking girth of QC LDPC codes with superposition matrices, and propose new decoder to support layered decoding both for original QC LDPC codes and their modifications with superposition matrices. Simulation results show considerable improvements to convergence speed and error-correcting performance of proposed scheme which adopts QC LDPC codes with superposition matrices.

• The Korean Journal of Ceramics
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• v.1 no.3
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• pp.152-154
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• 1995

A non-hydrolytic sol-gel process was developed to fabricate low-hydroxyl hard gels. The reaction of tert-butyl alcohol with silicon halides provided transparent low-hydroxyl hard gels. Some properties such as transparency, density, and refractive index was successfully doped into the hard gel matrices. The absorption spectrum of an erbium-doped methylsilsesquioxane was investigated to decide the pumping wavelength of an argon laser. The luminescence of the erbium-doped gel at 664 nm seems to be due to $4^F{9/2}\to 4^I_{15/2}$ transition.