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A class of quantum low-density parity check codes by combining seed graphs

QUANTUM INFORMATION PROCESSING 2013年第6期12卷 2219-2239页

作者： Hwang, Yongsoo Chung, Youngjoo Jeon, Moongu Gwangju Inst Sci & Technol Sch Informat & Commun Kwangju South Korea

This paper proposes a new construction of quantum low-density parity check (LDPC) codes that belong to the class of general stabilizer (non-CSS) codes. The method constructs a binary check matrix associated with the stabilizer generators of a quantum LDPC code. The binary check matrix is obtained from a large bipartite graph built by combining several small bipartite graphs called seed graphs. Computer simulation results show that the proposed code has similar or better performance than other quantum LDPC codes, and can be improved by exploiting the degenerate effect of quantum error-correcting codes.

关键词： Quantum error-correcting code General stabilizer (non-CSS) code low-density parity check code

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Scalable Globally-Coupled low-density parity check codes 10

Scalable Globally-Coupled Low-Density Parity Check Codes

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10th IEEE International Symposium on Turbo codes & Iterative Information Processing (ISTC)

作者： Liao, Yen-Chin Chang, Hsie-Chia Lin, Shu Natl Chiao Tung Univ Hsinchu Taiwan Univ Calif Davis Davis CA 95616 USA

ISBN: (纸本)9781538670484

This paper presents a technique to scale up an LDPC code to any desired block length. Under certain constraints, the scaled LDPC code results in a special case of globally-coupled-LDPC code. The proposed scheme can construct globally-coupled-LDPC codes from any short LDPC codes. A design example targeting for NAND flash memory applications is addressed and simulated. The results show the feasibility of constructing a structural long LDPC code by scaling from a short code.

关键词： low-density parity check code length-scalable LDPC code

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Informed shuffled belief- propagation decoding for low-density parity-check codes

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IET COMMUNICATIONS 2015年第18期9卷 2259-2266页

作者： Gong, Yi Liu, Xingcheng Han, Guojun Wu, Bin Sun Yat Sen Univ Sch Math & Computat Sci Guangzhou 510275 Guangdong Peoples R China Sun Yat Sen Univ Dept Elect & Commun Engn Guangzhou 510275 Guangdong Peoples R China Guangdong Univ Technol Sch Informat & Engn Guangzhou 510006 Guangdong Peoples R China

Shuffled belief propagation (SBP), as a sequential belief propagation (BP) algorithm, speeds up the convergence of BP decoding, and maintains the least complexity of flooding BP. However, its performance is remarkably inferior to informed dynamic scheduling (IDS) BP algorithms. The authors design an informed dynamic location method, based on the residuals of variable node log-likelihood ratio values, to reorder variable nodes of SBP to be updated. The location method significantly accelerates the convergence of SBP algorithm from two aspects: the unstable variable node with the largest residual to be updated first, and selecting the largest residual locally. Simulation results show that the proposed algorithm performs nearly the same as the best performance of IDS BP algorithms, and behaves prominently at high signal-to-noise ratios.

关键词： belief networks parity check codes telecommunication scheduling maximum likelihood decoding convergence informed shuffled belief propagation decoding low-density parity check code sequential belief propagation BP decoding flooding BP informed dynamic scheduling BP algorithm informed dynamic location method variable node log likelihood ratio value reorder variable node SBP algorithm convergene signal-to-noise ratio

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The Study of Induction Setter Based on low density parity check Coding Method

The Study of Induction Setter Based on Low Density Parity Ch...

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3rd International Conference on Advanced Design and Manufacturing Engineering (ADME 2013)

作者： Liu, Fuxiang Wang, Liumin Zhang, Feng Xu, Xiaomei Beijing Inst Technol Sch Aerosp Engn Beijing 100081 Peoples R China Chinese Acad Sci Inst Automat Beijing 100081 Peoples R China

ISBN: (纸本)9783037858431

In order to improve anti-jamming capability and transmission efficiency of the inductive setter, a structured approach to construct several low density parity check(LDPC) codes is used in this paper. The LDPC codes have different error-correcting capability, and can timely correct BER which are generated during the transmission of channel. The simulation analysis show that the LDPC codes can effectively avoid retransmission of the codeword, and raise the Induction Setter anti-jamming capability and transmission efficiency. The method of LDPC codes used in the inductive setting can ensure the control information efficiently load to the fuse.

关键词： Error correction coding low-density parity check code inductive setting

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low-complexity feedback-channel-free distributed video coding using local rank transform

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IET IMAGE PROCESSING 2017年第2期11卷 126-134页

作者： Bhagath, Pudi Raj Mallick, Kallol Mukherjee, Jayanta Mukopadhayay, Sudipta Indian Inst Technol Dept Elect & Elect Commun Engn Kharagpur W Bengal India Azure Software Syst Ltd Kolkata India Indian Inst Technol Dept Comp Sci & Engn Kharagpur W Bengal India

In this study, the authors propose a new feedback-channel-free distributed video coding algorithm using local rank transform (LRT). The encoder computes LRT by considering selected neighbourhood pixels of Wyner-Ziv (WZ) frame. These LRT values are merged, and their positions are entropy coded and sent to the decoder. In addition, means of each block of WZ frame are also transmitted to assist motion estimation (ME). Using these measurements, the decoder generates side information (SI) by implementing ME and compensation in LRT domain. An iterative algorithm is executed on SI using LRT to reconstruct the WZ frame. Experimental results show that the coding efficiency of the authors' codec is close to the efficiency of pixel domain distributed video coders based on low-density parity check and accumulate or turbo codes, with less encoder and decoder complexity.

关键词： video coding entropy codes turbo codes transforms motion estimation image resolution image reconstruction parity check codes turbo code accumulate code low-density parity check code pixel domain distributed video coders coding efficiency side information generation motion estimation WZ frame reconstruction Wyner-Ziv frame neighbourhood pixels LRT computation local rank transform low-complexity feedback-channel-free distributed video coding algorithm

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Joint phase noise estimation and data detection in coded multi-input-multi-output systems

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IET COMMUNICATIONS 2014年第7期8卷 981-989页

作者： Isikman, Arif O. Mehrpouyan, Hani Nasir, Ali A. Amat, Alexandre G. Kennedy, Rodney. A. Chalmers Univ Technol Commun Syst Grp S-41296 Gothenburg Sweden Calif State Univ Dept Elect & Comp Engn Bakersfield CA USA Australian Natl Univ Res Sch Engn Canberra ACT Australia

The problem of joint oscillator phase noise (PHN) estimation and data detection for multi-input multi-output (MIMO) systems using bit-interleaved-coded modulation is analysed. A new MIMO receiver that iterates between the estimator and the detector, based on the expectation-maximisation (EM) framework, is proposed. It is shown that at high signal-to-noise ratios, a maximum a posteriori (MAP) estimator can be used to carry out the maximisation step of the EM algorithm. Moreover, to reduce the computational complexity of the proposed EM algorithm, a soft decision-directed extended Kalman filter-smoother (EKFS) is applied instead of the MAP estimator to track the PHN parameters. The numerical results show that by combining the proposed EKFS-based approach with an iterative detector that employs low-density parity check codes, PHN can be accurately tracked. The simulations also demonstrate that compared to the existing algorithms, the proposed iterative receiver can significantly enhance the performance of MIMO systems in the presence of PHN.

关键词： phase noise MIMO communication radio receivers interleaved codes oscillators expectation-maximisation algorithm maximum likelihood estimation Kalman filters parity check codes iterative methods data detection coded multi-input-multi-output system joint oscillator phase noise estimation PHN estimation MIMO receiver bit-interleaved-coded modulation expectation-maximisation EM algorithm signal-to-noise ratio maximum a posteriori MAP estimator soft decision-directed extended Kalman filter-smoother EKFS-based approach low-density parity check code iterative receiver

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low-complexity graph-based turbo equalisation for single-carrier and multi-carrier FTN signalling

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IET SIGNAL PROCESSING 2017年第7期11卷 838-845页

作者： Yu, Tianhang Zhao, Minjian Zhong, Jie Zhang, Jian Xiao, Pei Zhejiang Univ Coll Informat Sci & Elect Engn Hangzhou 310027 Zhejiang Peoples R China Univ Surrey Inst Commun Syst Home Innovat Ctr 5G Guildford GU2 7XH Surrey England

The authors propose a novel turbo detection scheme based on the factor graph (FG) serial-schedule belief propagation equalisation algorithm with low complexity for single-carrier faster-than-Nyquist (SC-FTN) and multi-carrier FTN (MC-FTN) signalling. In this work, the additive white Gaussian noise channel and multi-path fading channels are both considered. The iterative FG-based equalisation algorithm can deal with severe intersymbol interference and intercarrier interference introduced by the generation of SC and MC-FTN signals, as well as the effect of multi-path fading. With the application of Gaussian approximation, the complexity of the proposed equalisation algorithm is significantly reduced. In the turbo detection, low-density parity check code is employed. The simulation results demonstrate that the FG-based turbo detection method can achieve satisfactory performance with low complexity.

关键词： graph theory fading channels intersymbol interference intercarrier interference approximation theory parity check codes AWGN channels low-complexity graph-based turbo equalisation FTN signalling factor graph serial-schedule belief propagation equalisation algorithm additive white Gaussian noise channel multipath fading channels iterative FG-based equalisation algorithm intersymbol interference intercarrier interference Gaussian approximation low-density parity check code FG-based turbo detection method

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Improved algorithm for joint detection and decoding on the joint sparse graph for CDMA systems

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IET COMMUNICATIONS 2016年第3期10卷 336-345页

作者： Wen, Lei Lei, Jing Su, Man Natl Univ Def Technol Coll Elect Sci & Engn Changsha Hunan Peoples R China Univ Surrey Inst Commun Syst Innovat Ctr 5G Guildford GU2 5XH Surrey England

Joint sparse graph for code division multiple access systems (JSG-CDMA) combines multiple accessing (low-density signature) and forward error correction (low-density parity check code) techniques, and it achieves satisfactory performance under overloaded conditions. In this study, the authors carry on the research on the joint detection and decoding for JSG-CDMA, and analyse the syndrome effect of message passing on the JSG by the extrinsic information transfer (EXIT) chart. An improved algorithm for joint detection and decoding on the JSG-CDMA receiver is proposed, and the convergence behaviour of the algorithm is analysed by EXIT chart. Simulation results show that improved algorithm enhance the system performance significantly with a marginal increase of the computational complexity.

关键词： communication complexity message passing parity check codes forward error correction decoding code division multiple access graph theory joint sparse graph decoding code division multiple access system forward error correction low-density parity check code low-density signature message passing effect extrinsic information transfer chart EXIT chart joint detection algorithm JSG-CDMA receiver computational complexity

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On the construction of stabilizer codes with an arbitrary binary matrix

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QUANTUM INFORMATION PROCESSING 2013年第1期12卷 467-479页

作者： Hwang, Yongsoo Choi, Byung-Soo Jeon, Moongu Gwangju Inst Sci & Technol Dept Informat & Commun Kwangju South Korea Duke Univ Dept Elect & Comp Engn Durham NC USA

This paper proposes a simple framework for constructing a stabilizer code with an arbitrary binary matrix. We define a relation between A (1) and A (2) of a binary check matrix A = (A (1)|A (2)) associated with stabilizer generators of a quantum error-correcting code. Given an arbitrary binary matrix, we can derive a pair of A (1) and A (2) by the relation. As examples, we illustrate two kinds of stabilizer codes: quantum LDPC codes and quantum convolutional codes. By the nature of the proposed framework, the stabilizer codes covered in this paper belong to general stabilizer (non-CSS) codes.

关键词： Quantum error-correcting code Stabilizer code low-density parity check code Convolutional code

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Small stopping sets in Steiner triple systems

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CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES 2009年第1期1卷 31-46页

作者： Colbourn, Charles J. Fujiwara, Yuichiro Arizona State Univ Tempe AZ 85287 USA Nagoya Univ Grad Sch Informat Sci Chikusa Ku Nagoya Aichi 4648601 Japan

The size of the smallest stopping set in a low-density parity check (LDPC) code determines, to an extent, the performance of iterative decoding methods over the binary erasure channel. In an LDPC code arising from a block design, a stopping set is a subset of its blocks with the property that every point belonging to one of the selected blocks belongs to at least two of them. While some Steiner triple systems have no stopping sets of size 5 or less, it is shown that every Steiner triple system has a stopping set of size at most 7. The proof can be viewed as an application of polynomial identities among configuration counts that generalize the family of known linear identities. While no example of a Steiner triple system whose smallest stopping set has size seven is known, it is shown that a partial Steiner triple system on v points with c . v(1.8) triples that has no stopping set of size less than 7 exists.

关键词： Stopping sets Steiner triple systems low-density parity check code

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