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International Conference on Software, Telecommunications and Computer Networks (SoftCOM)

On the generator matrix of array LDPC codes

Baldi Baldi, Valentina Bianchi, Cancellieri, Chiaraluce, Klove

Published Jan 1, 2012• 0 citations
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In this paper a new low complexity method for constructing binary quasi-cyclic low-density parity-check (QC-LDPC) codes is introduced. In the proposed method, each block-column of the parity check matrix H is made by a circulant matrix in a way that the associated Tanner graph is free of cycle four. Each circulant matrix in H is made by a generator column. The generator columns should be selected in a way that each associated circulant matrix and every two distinct circulant matrices are free of cycle four. The generator columns are made by row distance sets. An algorithm for generating distance sets and obtaining circulant matrices with columns of weight three is presented separately. Simplicity of construction and having a good flexible family of quasi cyclic LDPC codes both in rate and length are the main properties of the proposed method. The performance of the proposed codes is compared with that of the random-like and Array LDPC codes over an AWGN channel. Simulation results show that from the performance perspective, the constructed codes are competitive with random-like and Array LDPC codes.

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In this paper we present a general expression for the generator matrix of array low-density parity-check codes. This is a further contribution towards understanding the inner structure of these codes. Moreover, it represents a useful tool that can be used in the estimation and optimization of their minimum distance, which is an open problem. By using the new form of the generator matrix, we derive some necessary conditions on the maximization of the minimum distance.

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In this paper, we analyze the size of the smallest stopping set (called the stopping distance) for the parity-check matrix of a superposed array low-density parity-check (SA-LDPC) code for column weights 3 and 4 by using the transversal design (TD) concept. An SA-LDPC code is obtained as the result of an n-fold recursive product operation (a superposition method) on the parity-check matrix of an array low-density parity-check (array LDPC) code, Hn(m, q), where n ≥ 2 and m and q are column and row weights, respectively. We provide the lower and upper bounds for the stopping distance of these codes. Our simulation result shows that the SA-LDPC codes can compete with the TD-LDPC codes, random LDPC codes, and lattice LDPC codes of comparable rates and lengths and can improve the error floor region of the bit error rate curve.

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On the Construction and Decoding of Cyclic LDPC Codes

Chao Chen

•Jan 1, 2014•0 citations
In this paper a new low complexity method for constructing binary quasi-cyclic low-density parity-check (QC-LDPC) codes is introduced. In the proposed method, each block-column of the parity check matrix H is made by a circulant matrix in a way that the associated Tanner graph is free of cycle four. Each circulant matrix in H is made by a generator column. The generator columns should be selected in a way that each associated circulant matrix and every two distinct circulant matrices are free of cycle four. The generator columns are made by row distance sets. An algorithm for generating distance sets and obtaining circulant matrices with columns of weight three is presented separately. Simplicity of construction and having a good flexible family of quasi cyclic LDPC codes both in rate and length are the main properties of the proposed method. The performance of the proposed codes is compared with that of the random-like and Array LDPC codes over an AWGN channel. Simulation results show that from the performance perspective, the constructed codes are competitive with random-like and Array LDPC codes.
In this paper, we analyze the size of the smallest stopping set (called the stopping distance) for the parity-check matrix of a superposed array low-density parity-check (SA-LDPC) code for column weights 3 and 4 by using the transversal design (TD) concept. An SA-LDPC code is obtained as the result of an n-fold recursive product operation (a superposition method) on the parity-check matrix of an array low-density parity-check (array LDPC) code, Hn(m, q), where n ≥ 2 and m and q are column and row weights, respectively. We provide the lower and upper bounds for the stopping distance of these codes. Our simulation result shows that the SA-LDPC codes can compete with the TD-LDPC codes, random LDPC codes, and lattice LDPC codes of comparable rates and lengths and can improve the error floor region of the bit error rate curve.