IEEE Vehicular Technology Conference

Construction of LDPC Codes Based on Narrow-Sense-Primitive BCH Codes

Yi Yu, Liu Shaobo, Huang Dawei

Published Dec 10, 2005• 5 citations

Abstract

In this paper, we present an algebraic method for constructing regular low-density parity-check (LDPC) codes based on narrow-sense-primitive BCH codes. The construction method results in a class of high rate LDPC codes in Gallager's original form. Codes in this class are free of cycles of length 4 in their Tanner graph and have good minimum distances. They can perform well with the iterative decoding. Also, proposed algebra LDPC codes can be designed for a new class of irregular codes based on a semi-algebraic structure for various code rates. It is shown that, with the proposed construction algorithms, fast construction time and reduced memory without the performance degradation can be achieved.

DOI: 10.1109/vetecs.2005.1543584

Related papers

Families of LDPC Codes Derived from Nonprimitive BCH Codes and Cyclotomic Cosets

Salah A. Aly

Low-density parity check (LDPC) codes are an important class of codes with many applications. Two algebraic methods for constructing regular LDPC codes are derived -- one based on nonprimitive narrow-sense BCH codes and the other directly based on cyclotomic cosets. The constructed codes have high rates and are free of cycles of length four; consequently, they can be decoded using standard iterative decoding algorithms. The exact dimension and bounds for the minimum distance and stopping distance are derived. These constructed codes can be used to derive quantum error-correcting codes.

arXiv:0802.4079Feb 27, 20087 citations

The Design of Structured Low-Density Parity-Check Codes With Large Girth

Jing Long

This paper,based on algebra and graph,proposes a method for constructing structured low-density parity-check(LDPC) codes.In this method,the authors design a connected graph with three kinds of special path to ensure that the Tanner graph of the parity check matrix mapped from the connected graph is without short cycles.The construction method results in two classes of(3,k)-regular quasi-cyclic LDPC codes with girth 8 and 12 respectively.Furthermore,by extending this construction method,two classes of LDPC codes with column weight 2,whose girths are respectively 16 and 24,can be obtained.The simulation studies show that these codes can achieve better performance than randomly constructed regular LDPC codes over AWGN channels with iterative decoding.At the BER of 10-5,the new proposed(3,6)-regular(4356,2205) QC-LDPC code performs 1.48dB from the Shannon limit.Moreover,it outperforms the random regular LDPC code of comparable parameters by 0.1dB.For the new proposed structured LDPC codes with column weight 2,they can achieve about 2dB coding gains with respect to the random regular LDPC codes with similar block lengths and code rates.

Chinese Journal of ComputersJan 1, 20071 citation

A Class of Improved Low-Density Parity-Check Codes Constructed Based on Gallager's Form

Guangen Wu, Pinyi Ren

Focused on the problem that short cycles degrade the iterative decoding performance of finite length LDPC, a class of improved low density parity check (LDPC) codes constructed based on Gallager's form is designed. On the basis of keeping down the basic form of Gallager's construction, a quasi-cyclic form is used, then the new codes are free of cycles of length 4 and have good minimum distance. Simulation results demonstrated that the improved codes are better than Gallager's codes when block length is small

International Conference on Communications, Circuits and SystemsJun 1, 20060 citations

Recursive construction of LDPC codes

Shunliang Mei

To reduce the cycles in the Tanner graph which may affect the code performance,a recursive method to construct low-density parity-check(LDPC) codes was proposed.The method used a parity-check matrix of a short LDPC code as its mother matrix upon which a long code was constructed with circulant permutation matrices.By choosing the circulant permutation matrix parameters properly,the number of cycles having a given length in the Tanner graph of the constructed long codes were equal to or less than that of the short code.Either regular or irregular LDPC codes were constructed.Simulation results show that the LDPC codes constructed by this method have very low error-floor and almost no performance degradation due to their special structure as compared with random LDPC codes.

Journal of Tsinghua University(Science and Technology)Jan 1, 20070 citations

A new random construction for low-density parity-check codes

Zhonghu Huang, Shen Lianfeng, Zhihui Ye

This paper gives a new random construction for LDPC codes, which uses an iterative algorithm to avoid short cycles in the Tanner graph. The construction method has low complexity and great flexible choice in LDPC code parameters including code length, code rate, least girth of the graph, and the weight of column and row in the parity-check matrix. The method can be applied to the irregular LDPC codes and strict regular LDPC codes. Simulations show that the method performs well with iterative decoding.

International Conference on Communications, Circuits and SystemsAug 16, 20050 citations

Classes of LDPC codes constructed from elements of finite fields and cyclotomic cosets

Salah A. Aly, Hussein H. Maza'ar

In this paper, we derive two algebraic methods for constructing regular low density parity check (LDPC) codes - one based on elements of finite fields and the other directly based on cyclotomic cosets. We show that the constructed codes have high rates and are free of cycles of length four; consequently, they can be decoded using standard iterative decoding algorithms. In addition we compute the exact dimension and establish bounds on the minimum and stopping distances of the constructed codes.

Canadian Workshop on Information Theory (CWIT)May 1, 20091 citation