Author:  Li, Miaolei 
Title:  Construction of QCLDPC codes with large girth 
Degree:  M.Sc. 
Year:  2012 
Subject:  Coding theory  Mathematics. Errorcorrecting 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 paritycheck matrices of quasicyclic lowdensity paritycheck (QCLDPC) 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) QCLDPC 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. 
Files  Size  Format 

b2471060x.pdf  2.119Mb 


As a bona fide Library user, I declare that:  


By downloading any item(s) listed above, you acknowledge that you have read and understood the copyright undertaking as stated above, and agree to be bound by all of its terms. 