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Girth 4 of Gallager codes

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The program shows the girth 4 of Gallager codes

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The Program to test the girth 4 of Gallager LDPC codes
Copyright (C) Yang XIAO, BJTU, July 26, 2007, E-Mail:,
The program analyzes the girth 4 for Gallager LDPC codes. The figures show
the parity check matrix H and the girth test matrix O, respectively.
Fig 1 can help us know the 1s’ distribution of the parity check matrix H.
Fig. 2 is the result of girth 4 for the given H.
Theorem in Ref [1]: The H matrix has no gith4, if and only if the O matrix in Fig.2 has no entry value to be larger than 1.
[1] Y. Xiao, M -H Lee, “Low complexity MIMO-LDPC CDMA systems over multipath channels”,
IEICE Transactions on Communications, v E89-B, n 5, May, 2006, p 1713-1717
[2] J. Fan, Y. Xiao, “A method of counting the number of cycles in LDPC codes”,
8th International Conference on Signal Processing, ICSP 2006,Volume: 3,
ISBN: 0-7803-9737-1, Digital Object Identifier: 10.1109/ICOSP.2006.345906
[3] MOHAMMED ALKHANBASH, Gallager LDPC, Matlab center, File Exchange, 2007
The papers [1] and [2] can be downloaded from Web site of IEICE and IEEE Explore.

Comments and Ratings (5)


Lomesh (view profile)

Hello Sir, could you please guide on how to construct a code to eliminate any girth-4 cycle in a parity-check matrix?
I have just started to learn LDPC.

silvia anggraeni

Thank you for giving the simple m-file to test girth 4 cycle. It is very useful for me and my program .....

Yang Xiao

Reply to Mr. Arash Saber:

My program is only to show that the published Gallager codes have girth 4, the problem is ignored by many LDPC learners.

From your comment, I suppose, you may not know the girth 4 problem of LDPC codes.

Arash Saber

Is this your first time writing a program?

B. Roossien

- Script file
- Contains the 'clear' command
- Useless data is not supressed by a semicolon
- No pre-allocation of growing arrays.

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