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Ternary Codes from Modified Jacket Matrices
Jiang, Xueqin,Lee, Moon-Ho,Guo, Ying,Yan, Yier,Latif, Sarker Md. Abdul The Korea Institute of Information and Commucation 2011 Journal of communications and networks Vol.13 No.1
In this paper, we construct two families $C^*_m$ and ${\~{C}}^*_m$ of ternary ($2^m$, $3^m$, $2^{m-1}$ ) and ($2^m$, $3^{m+1}$, $2^{m-1}$ ) codes, for m = 1, 2, 3, ${\cdots}$, derived from the corresponding families of modified ternary Jacket matrices. These codes are close to the Plotkin bound and have a very easy decoding procedure.
Design of Non-Binary Quasi-Cyclic LDPC Codes Based on Multiplicative Groups and Euclidean Geometries
Jiang, Xueqin,Lee, Moon-Ho The Korea Institute of Information and Commucation 2010 Journal of communications and networks Vol.12 No.5
This paper presents an approach to the construction of non-binary quasi-cyclic (QC) low-density parity-check (LDPC) codes based on multiplicative groups over one Galois field GF(q) and Euclidean geometries over another Galois field GF($2^S$). Codes of this class are shown to be regular with girth $6{\leq}g{\leq}18$ and have low densities. Finally, simulation results show that the proposed codes perform very wel with the iterative decoding.
Large Girth Non-Binary LDPC Codes Based on Finite Fields and Euclidean Geometries
Xueqin Jiang,Moon Ho Lee IEEE 2009 IEEE signal processing letters Vol.16 No.6
<P>This letter presents an approach to the construction of non-binary low-density parity-check (LDPC) codes based on alpha-multiplied circulant permutation matrices and hyperplanes of two different dimensions in Euclidean geometries. Codes constructed by this method have large girth and high binary column weight when the order of Galois field is high. Simulation results show that these codes perform very well with fast Fourier transform (FFT) based sum-product algorithm (SPA).</P>
Optimized Geometric LDPC Codes with Quasi-Cyclic Structure
Xueqin Jiang,이문호,Shangce Gao,Yun Wu 한국통신학회 2014 Journal of communications and networks Vol.16 No.3
This paper presents methods to the construction of regularand irregular low-density parity-check (LDPC) codes based onEuclidean geometries over the Galois field. Codes constructed bythese methods have quasi-cyclic (QC) structure and large girth. Bydecomposing hyperplanes in Euclidean geometry, the proposed irregularLDPC codes have flexible column/row weights. Therefore,the degree distributions of proposed irregular LDPC codes can beoptimized by technologies like the curve fitting in the extrinsic informationtransfer (EXIT) charts. Simulation results show that theproposed codes perform very well with an iterative decoding overthe AWGN channel.
Progressive Edge-Growth Algorithm for Low-Density MIMO Codes
Xueqin Jiang,Yi Yang,이문호,Minda Zhu 한국통신학회 2014 Journal of communications and networks Vol.16 No.6
In low-density parity-check (LDPC) coded multipleinputmultiple-output (MIMO) communication systems, probabilisticinformation are exchanged between an LDPC decoder and aMIMO detector. TheMIMO detector has to calculate probabilisticvalues for each bit which can be very complex. In [1], the authorspresented a class of linear block codes named low-density MIMOcodes (LDMC) which can reduce the complexity of MIMO detector. However, this code only supports the outer-iterations betweenthe MIMO detector and decoder, but does not support the inneriterationsinside the LDPC decoder. In this paper, a new approachto construct LDMC codes is introduced. The new LDMC codes canbe encoded efficiently at the transmitter side and support both ofthe inner-iterations and outer-iterations at the receiver side. Furthermorethey can achieve the design rates and perform very wellover MIMO channels.
Multiple-Rate Quasi-Cyclic LDPC Codes Based on Euclidean Geometries
JIANG, Xueqin,LEE, Moon Ho,SHIN, Tae Chol The Institute of Electronics, Information and Comm 2010 IEICE TRANSACTIONS ON COMMUNICATIONS - Vol.93 No.4
<P>This letter presents an approach to the construction of multiple-rate quasi-cyclic (QC) low-density parity-check (LDPC) codes based on hyperplanes (μ-flats) of two different dimensions in Euclidean geometries. The codes constructed with this method have the same code length, multiple-rate and large stopping sets while maintaining the same basic hardware architecture. The code performance is investigated in terms of the bit error rate (BER) and compared with those of the LDPC codes which are proposed in IEEE 802.16e standard. Simulation results show that our codes perform very well and have low error floors over the AWGN channel.</P>
Efficient Progressive Edge-Growth Algorithm Based on Chinese Remainder Theorem
Xueqin Jiang,Xiang-Gen Xia,Moon Ho Lee IEEE 2014 IEEE TRANSACTIONS ON COMMUNICATIONS Vol.62 No.2
<P>Progressive edge-growth (PEG) algorithm construction builds a Tanner graph, or equivalently a parity-check matrix, for an LDPC code by establishing edges between the symbol nodes and the check nodes in an edge-by-edge manner and maximizing the girth in a greedy fashion. This approach is simple but the complexity of the PEG algorithm scale is O(nm), where n is the number of symbol nodes and m is the number of check nodes. We deal with this problem by construct a base matrix H<SUB>b</SUB> of size m<SUB>b</SUB> × n<SUB>b</SUB> with the PEG algorithm and simultaneously expand this base matrix into a parity-check matrix H of size mx n via the the Chinese remainder theorem (CRT), where m ≫ m<SUB>b</SUB> and n ≥ n<SUB>b</SUB>. The size of the base matrix is expanded without decreasing the girth. For convenience, the PEG and CRT combined algorithm is referred to as the PEG-CRT algorithm in this paper. Since a smaller matrix is constructed with the PEG algorithm and the complexity of the CRT computation is negligible compared to the PEG algorithm, the complexity of the whole code construction process is reduced. Furthermore, the proposed algorithm has a potential advantage of saving storage space by storing a smaller matrix H<SUB>b</SUB> and expanding it to H 'on-the-fly' in hardware. The expanded matrix H preserves the important properties of base matrix such as large girth, flexible code rate and low density. The complexity analysis shows that the complexity of the PEG-CRT algorithm does not grow with the code length n. Simulation results show that compared with the PEG LDPC codes of length n<SUB>b</SUB>, the expanded PEG-CRT LDPC codes have better bit error rate (BER) performance with the iterative decoding. It is also shown that compared with PEG LDPC codes of length n, which constructed with higher complexities, the PEG-CRT codes have similar BER performance.</P>
Construction of Multiple-Rate Quasi-Cyclic LDPC Codes via the Hyperplane Decomposing
Jiang, Xueqin,Yan, Yier,Lee, Moon-Ho The Korea Institute of Information and Commucation 2011 Journal of communications and networks Vol.13 No.3
This paper presents an approach to the construction of multiple-rate quasi-cyclic low-density parity-check (LDPC) codes. Parity-check matrices of the proposed codes consist of $q{\times}q$ square submatrices. The block rows and block columns of the parity-check matrix correspond to the hyperplanes (${\mu}$-fiats) and points in Euclidean geometries, respectively. By decomposing the ${\mu}$-fiats, we obtain LDPC codes of different code rates and a constant code length. The code performance is investigated in term of the bit error rate and compared with those of LDPC codes given in IEEE standards. Simulation results show that our codes perform very well and have low error floors over the additive white Gaussian noise channel.