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One of the phenomena that causes high decoding failure rates is trappingsets. Characterization of $(a,b)$ elementary trapping sets (ETSs), theirgraphical properties and the lower bounds on their size in variable regularLDPC codes with column weights 3, 4, 5 and 6, where $a$ is the size of the ETSand $b$ is the number of degree-one check nodes, have been an interestingsubject among researchers. Although progressive-edge-growth method (PEG) toconstruct LDPC codes free of an specific ETS has been proposed in theliterature, it is mostly applied to LDPC codes with column weight 3. In thispaper, we focus on constructing QC-LDPC codes with column weight 4 whose Tannergraphs are free of small ETSs. Using coloring the edges of the variable node(VN) graph corresponding to an ETS, we provide the sufficient conditions toobtain QC-LDPC codes with column weight 4, girth 6 and free of $(5,b)$ ETSs,where $b\leq4$, and $(6,b)$ ETs, where $b\leq2$. Moreover, for $(4,n)$-regularQC-LDPC codes with girth 8, we present a method to remove $(7,4)$ ETSs fromTanner graphs.

Edge Coloring Technique to Remove Small Elementary Trapping Sets from Tanner Graph of QC-LDPC Codes with Column Weight 4