• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.2C
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• pp.173-177
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• 2008

In this paper, we improve performance of Low Density Parity Check (LDPC) codes with adding a large number of short cycles. Short cycles, especially cycles of length 4, degrade performance of LDPC codes if the standard BP (Belief Propagation) decoding is used. Therefore current researches have focused on removing cycles of length 4 for designing good performance LDPC codes. We found that a large number of cycles of length 4 improve performance of LDPC codes if a modified BP decoding is used. We present the modified BP decoding algorithm for LDPC codes with a large number of short cycles. We show that the modified BP decoding performance of LDPC codes with a large number of short cycles is better than the standard BP decoding performance of LDPC codes designed by avoiding short cycles.

• Journal of Communications and Networks
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• v.15 no.2
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• pp.217-221
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• 2013

Quantum low-density parity-check (LDPC) codes based on the Calderbank-Shor-Steane construction have low encoding and decoding complexity. The sum-product algorithm(SPA) can be used to decode quantum LDPC codes; however, the decoding performance may be significantly decreased by the many four-cycles required by this type of quantum codes. All four-cycles can be eliminated using the entanglement-assisted formalism with maximally entangled states (ebits). The proposed entanglement-assisted quantum error-correcting code based on Euclidean geometry outperform differently structured quantum codes. However, the large number of ebits required to construct the entanglement-assisted formalism is a substantial obstacle to practical application. In this paper, we propose a novel class of entanglement-assisted quantum LDPC codes constructed using classical Euclidean geometry LDPC codes. Notably, the new codes require one copy of the ebit. Furthermore, we propose a construction scheme for a corresponding zigzag matrix and show that the algebraic structure of the codes could easily be expanded. A large class of quantum codes with various code lengths and code rates can be constructed. Our methods significantly improve the possibility of practical implementation of quantum error-correcting codes. Simulation results show that the entanglement-assisted quantum LDPC codes described in this study perform very well over a depolarizing channel with iterative decoding based on the SPA and that these codes outperform other quantum codes based on Euclidean geometries.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.10C
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• pp.942-949
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• 2007

In this paper, we propose a new rate-control scheme, called splining, to construct low-rate codes from high-rate codes by splitting rows of the parity-check matrices of LDPC codes, which can construct rate-compatible LDPC codes having good initial transmission performance. Good low-rate codes can be constructed by making the number of distinct check node degrees as small as possible after splitting. The proposed scheme achieves good cycle property, low decoding complexity, and fast convergence speed, especially compared to the puncturing. Especially, rate-compatible repeat accumulate-type LDPC (RA-Type LDPC) code is constructed using splitting, which covers the code rates from 1/3 to 4/5. Through simulation it is shown that this code outperforms other rate-compatible RA-Type LDPC codes for all rates and can be decoded conveniently and efficiently.

• ETRI Journal
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• v.45 no.1
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• pp.7-17
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• 2023

The error-rate floor of low-density parity-check (LDPC) codes is attributed to the trapping sets of their Tanner graphs. Among them, fully absorbing sets dominantly affect the error-rate performance, especially for short blocklengths. Efficient methods to identify the dominant trapping sets of LDPC codes were thoroughly researched as exhaustively searching them is NP-hard. However, the existing methods are ineffective for Raptor-like LDPC codes, which have many types of trapping sets. An effective method to identify dominant fully absorbing sets of Raptor-like LDPC codes is proposed. The search space of the proposed algorithm is optimized into the Tanner subgraphs of the codes to afford time-efficiency and search-effectiveness. For 5G New Radio (NR) base graph (BG) 2 LDPC codes for short blocklengths, the proposed algorithm finds more dominant fully absorbing sets within one seventh of the computation time of the existing search algorithm, and its search-effectiveness is verified using importance sampling. The proposed method is also applied to 5G NR BG1 LDPC code and Advanced Television Systems Committee 3.0 type A LDPC code for large blocklengths.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.41 no.5
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• pp.504-511
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• 2016

In this paper, MIMO system based on turbo equalization techniques which LDPC codes were outer code and space time trellis codes (STTC) were employed as an inner code are studied. LDPC decoder and STTC decoder are connected through the interleaving and de-interleaving that updates each other's information repeatedly. In conventional turbo equalization of MIMO system, BCJR decoder which decodes STTC coded bits required two-bit wise decoding processing. Therefore duo-binary turbo codes are optimal for MIMO system combined with STTC codes. However a LDPC decoder requires bit unit processing, because LDPC codes can't be applied to these system. Therefore this paper proposed turbo equalization for MIMO system based on LDPC codes combined with STTC codes. By the simulation results, we confirmed performance of proposed turbo equalization model was improved about 0.6dB than that of conventional LDPC codes.

• 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 Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.3A
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• pp.207-213
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• 2006

In this paper, we reduce the computational complexity to find the minimum distance of RA codes by searching only valid codewords using repetition part. Since LDPC codes have repetition part like RA codes, we also apply this algorithm for computing the minimum distance of LDPC codes. The minimum distance dominates the code performance at high signal-to-noise ratios(SNRs) and in turn allows an estimate of the error floor. The proposed algorithm computes the minimum distance without any constraint on code structures. The minimum distances of LDPC codes and RA codes with large interleavers of practical importance are computed and used to obtain the error floor, which is compared with the performance of the iterative decoding.

• Journal of Communications and Networks
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• v.17 no.4
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• pp.346-350
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• 2015

It is known that the progressive edge-growth (PEG) algorithm can be used to construct low-density parity-check (LDPC) codes at finite code lengths with large girths through the establishment of edges between variable and check nodes in an edge-by-edge manner. In [1], the authors derived a class of LDPC codes for relay communication systems by extending the full-diversity root-LDPC code. However, the submatrices of the parity-check matrix H corresponding to this code were constructed separately; thus, the girth of H was not optimized. To solve this problem, this paper proposes a modified PEG algorithm for use in the design of large girth and full-diversity LDPC codes. Simulation results indicated that the LDPC codes constructed using the modified PEG algorithm exhibited a more favorable frame error rate performance than did codes proposed in [1] over block-fading channels.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.12C
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• pp.1129-1134
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• 2006

In this paper, we analyze the cycle structure of punctured finite-length RA-type LDPC codes and design interleavers which have good memory efficiency and avoid short cycles. Furthermore, we introduce the check-node merging scheme for punctured finite-length RA-type LDPC codes and design simple interleavers. Simulation results show that punctured finite-length RA-type LDPC codes using the proposed simple interleavers have better performance than those with random and S-random interleavers.

• Proceedings of the IEEK Conference
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• 2008.06a
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• pp.14-15
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• 2008

In this paper, a new iterative decoding of LDPC codes is proposed. The decoding is based on the posteriori probability of each belief propagation (BP) decoding and an additional postprocessing, that is, erasure decoding of LDPC codes. It turned out that the new method consistently improves the decoding performance on various classes of LDPC codes. For example it removes the error floor of Margulis codes effectively.