Construction of QC-LDPC codes with large girth

Pao Yue-kong Library Electronic Theses Database

Construction of QC-LDPC codes with large girth

 

Author: Li, Miaolei
Title: Construction of QC-LDPC codes with large girth
Degree: M.Sc.
Year: 2012
Subject: Coding theory -- Mathematics.
Error-correcting codes (Information theory)
Hong Kong Polytechnic University -- Dissertations
Department: Dept. of Electronic and Information Engineering
Pages: xi, 85 leaves : ill. ; 30 cm.
Language: English
InnoPac Record: http://library.polyu.edu.hk/record=b2471060
URI: http://theses.lib.polyu.edu.hk/handle/200/6371
Abstract: In this report, we use Fibonacci sequences to fill the exponent matrices of the parity-check matrices of quasi-cyclic low-density parity-check (QC-LDPC) codes. Using the Fibonacci sequences, the corresponding LDPC code has no cycle 4.Using the Fibonacci sequences, we can easily construct codes with girth 8. Simulation results show that over an Additive White Gaussian Noise (AWGN) channel, the error performance of our code is much better than that of array codes. The LDPC code using Fibonacci sequence can achieve much lower bit error rate (BER) than that of array codes. Then we improve the method of using Fibonacci sequence to the method of using a combination of Fibonacci sequence and A.P. (Arithmetic Progression). Simulation results show that error performance of code using Fibonacci sequence and A.P. is almost the same as that of using Fibonacci sequence only. We find a new type of code that can perform as well as the code using Fibonacci sequence only. Then we improve the method of using Fibonacci sequence only to the method of using a combination of Fibonacci sequence and G.P. (Geometric Progression). For (3,6) QC-LDPC code, the error performance of code using Fibonacci sequence only is much worse than that of code using a combination of Fibonacci sequence and G.P. Next we propose the definition of 1st order difference Fibonacci sequence. Then we improve the Fibonacci sequence method to the method of using a combination of Fibonacci sequence and 1st order difference Fibonacci sequence. Simulation results show that the error performance of using Fibonacci sequence and 1st order difference Fibonacci sequence is much better than that of using Fibonacci sequence only. Then we propose a method that can avoid cycle 6 using the Fibonacci sequence. Last but not least, we contrast the influence on cycles of 5 kinds of construction functions. We draw the conclusion that the construction function f(i,j) = a ʲ⁻¹ b ⁱ⁻¹ the best form. So if we want to construct LDPC codes with large girth, we can use the form f(i,j) = a ʲ⁻¹ b ⁱ⁻¹ directly. There is no need for us to try other kinds of construction functions.

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