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IEICE Transactions on Communications

Multiple-Rate Quasi-Cyclic LDPC Codes Based on Euclidean Geometries

Xueqin Jiang, Moon Ho Lee, Tae Chol Shin

Published Jan 1, 2010• 0 citations
Publisher

Abstract

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.

DOI
10.1587/transcom.e93.b.997

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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.
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 X q square submatrices. The block rows and block columns of the parity-check matrix correspond to the hyperplanes (μ-flats) and points in Euclidean geometries, respectively. By decomposing the μ -flats, 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.
A new method for constructing quasi-cyclic (QC) low-density parity-check (LDPC) codes based on the structural properties of Euclidean geometries is presented. The proposed method changes the incidence vectors of some lines in the original Euclidean geometry method to construct much more parity check matrices and results in a large class of QC-LDPC codes with girth of at least 6. Simulations show that some codes in this class have better performance and lower error floor than the original Euclidean geometry codes.
This paper presents a method to the construction of irregular low-density parity-check (LDPC) codes based on Euclidean geometries over the Galois field. Codes constructed by this method are quasi-cyclic (QC) and have large girths. The proposed irregular LDPC codes having flexible column/row weights are obtained with a hyperplane decomposing method in Euclidean geometries. Therefore, the degree distributions of proposed irregular LDPC codes can be optimized by technologies like the curve fitting approach in the extrinsic information transfer (EXIT) charts. Simulation results show that these codes perform very well with an iterative decoding over the AWGN channel.
This paper presents methods to the construction of regular and irregular low-density parity-check (LDPC) codes based on Euclidean geometries over the Galois field. Codes constructed by these methods have quasi-cyclic (QC) structure and large girth. By decomposing hyperplanes in Euclidean geometry, the proposed irregular LDPC codes have flexible column/row weights. Therefore, the degree distributions of proposed irregular LDPC codes can be optimized by technologies like the curve fitting in the extrinsic information transfer (EXIT) charts. Simulation results show that the proposed codes perform very well with an iterative decoding over the AWGN channel.