Suppose that we have a LDPC code $C$ with a $(n -k )\times n $ parity check matrix $H$, and there exist approximately $ \sqrt n$ numbers of degree-2 columns. It means that there are approximately $\sqrt n$ numbers of degree-2 variable nodes($VN$) in the corresponding Tanner graph. 


We suppose that the left $VN$s are with high degrees, and then $C$ is irregular. The girth of $C$ is $\geq 8$. 


I want to know that whether these degree-2 $VN$s will affect the decoding performance seriously. What kind of effects will it have? Such as high error floors, degradation in the waterfall region? 


Sincerely,  

Bruce 



Effects of many degree-2 variable nodes in the Tanner graph during the decoding of LDPC codes
As maybe you know, the most good decoding algorithm for LDPC codes, for example iterative decoding, has not provable efficiency, except in special cases. But, it is believed that variable nodes with degree $2$, behave weaker in error protection against the higher degree variable nodes. Also, the important part of efficiency of the decoding algorithms depends to the first round executing. So, degree $2$ variable nodes shows their effects in the first stage for the failing of the algorithm.


For more details you can see the book:


"LDPC Coded Modulations" by "Michele Franceschini, Gianluigi Ferrari, Riccardo Raheli"


Also, there are some good references in the book which help you for finding good answer for your question.


Note that, the degree $2$ variable nodes effect on trapping sets and stopping sets of the LDPC codes which are good parameters for the efficiency of the decoding algorithm. 


