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International Conference on Communications, Circuits and Systems

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

Guangen Wu, Pinyi Ren

Published Jun 1, 2006• 0 citations
Publisher

Abstract

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

DOI
10.1109/icccas.2006.284750

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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
The existing design of quasi-cyclic low-density parity-check(short for QC-LDPC) codes has not considered the problems of small stopping sets and small cycles together,while their existences will lead to the BER performance of QC-LDPC codes to be much poorer than that of the randomly constructed LDPC codes even decoding failure.To solve the problem,some theorems of the QC-LDPC codes without small stopping sets and small cycles were proposed which provide a theoretical basis for the construction of parity-check matrix by analysis method;meanwhile,good QC-LDPC codes without small stopping sets and small cycles were designed.Since preventing the small stopping sets and small cycles also prevents a low minimum distance,our construction method also leads to QC-LDPC codes with a higher minimum distance.The simulation results show that the QC-LDPC codes can effectively avoid specified stopping sets and small cycles and achieve good coding and decoding property due to the proposed constructions.
Short cycles in the Tanner graph of a given LDPC code has negative effect on the performance of iterative decoding. To improve the performance, we presented an approach for constructing Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes whose associated Tanner graph has large girth and a small amount of short cycles. Each column block of the parity check matrix was designed by adding circulant permutation sub-matrices one after another, provided the current parity check matrix has minimal number of short cycles. The condition for the proposed QC-LDPC codes to have girth at least 6 was also analyzed. Regular and irregular QC-LDPC codes with various lengths and rates can be constructed. Simulations show that the proposed QC-LDPC codes have less short cycles and better performance than existing progressive edge growth based QC-LDPC codes.
This paper presents an improved Euclidean geometry (EG) method for constructing parity check matrix of quasi-cyclic low-density parity-check (QC-LDPC) codes to decrease the performance degradation of short cycles to the iterative decoding. The new method results in a class of QC-LDPC codes with much fewer short cycles than usual EG-LDPC codes with the same parameters. Simulation results show that the designed QC-LDPC codes with fewer short cycles perform better than the existing Euclidean geometry LDPC codes under iterative decoding.
In this paper,two classes of partially balanced incomplete block designs (PBIBD) based on finite fields is constructed,and they are used to construct the regular low-density parity-check (LDPC) codes.The constructed LDPC codes are free of 4-cycles and with high flexibility for choosing the code rate.In particular,they can also be quasi-cyclic.Simulations show that the constructed LDPC codes under sum-product iterative decoding perform very well over additive white Gaussian noise (AWGN) channels with BPSK modulation.
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.
Two classes of well-structured binary low-density parity check codes (LDPC) are described. The first class is based on a branch of combinatorial mathematics, known as the balanced incomplete block design (BIBD). Construction of three types of codes derived from BIBD designs is illustrated in addition to a family of LDPC codes constructed by decomposition of incidence matrices of the proposed BIBD designs. The decomposition technique reduces the density of the parity check matrix and hence reduces the number of short cycles, which generally lead to better performing LDPC codes. The second class of well-structured LDPC codes, Vandermonde or array LDPC codes, are defined by a small number of parameters and cover a large set of code lengths and rates with different column weights. The presented LDPC codes are quasi-cyclic with no cycles of length four; hence simple encoding while maintaining good performance is achieved. Furthermore, the codes are compared with known random LDPC codes, in order to assess their relative achievable performance/complexity trade-offs. It is shown that well-structured LDPC codes perform very similar to the known random LDPC codes.