On The Tree-based Construction Of Regular LDPC Codes

The low density parity check (LDPC) codes are a class of linear block codes based on the sparse check matrix, which is proposed by R. G. Gallager in 1962. They are good codes for their performance approaching Shannon limits, with the characteristics of convenient description, easy theoretical analysis, simple decoding and a good prospect etc., in recent years, they have been widespread concerned.In the study of iterative decoding of LDPC codes, it has been found that the pseudoweight of LDPC codes and short cycles in a Tanner graph have an important role in decoding. The larger minimal pseudoweight, the smaller probability of decoding error. While short cycles in Tanner graph could reduce the decoding performance, therefore, short cycles should be avoided in the construction of LDPC codes as possible as we can.In the thesis, we give the complete proof process of the low bound of the minimal pseudoweight, but is not proved wholely. Then we discuss the construction of d-regular LDPC codes when the layer of trees is arbitrary, which is promised by their layer 3 and 4 trees based constructions and yields girth 6 or 8 Tanner graphs, as the same as Kelley et al did. After that, we present a construction of regular LDPC codes of 3 column weight, which is based on odd layer trees and yields no 4-cycle Tanner graphs, we also give examples for every construction.