Row and Column Extensions of 4-Cycle Free LDPC Codes
Mohammad Reza Gholami, Akram Nassaj · IEEE Communications Letters · 2015
In this letter, an approach is proposed to increase the row (column)-weight of the parity-check matrix of a 4-cycle free LDPC code such that the constructed LDPC code has girth of at least 6. In fact, to each parity-check matrix H, a new graph Gr(H) (Gc(H)) is assigned in which the vertices correspond to the rows (columns) of H and two vertices are adjacent if and only if the associated rows (columns) have in common at least one nonzero element. Now, in a proper vertex coloring of Gr(H) (Gc(H)), each color is considered as a new column (row) whose nonzero elements happen in the rows (columns) in which the corresponding vertices have the same color. Based on this method, some high-rate LDPC codes with girth 6 and column-weight of at least 4 can be constructed from the recently proposed column-weight three LDPC codes with girth 6. Moreover, using the mutually orthogonal Latin squares, this approach is applied on the incidence matrices of some complete bipartite graphs to generate some girth-6 LDPC codes with different column-weights and large minimum-distances.