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Generating random Tanner-graphs with large girth

We present a simple and efficient algorithm for randomly generating Tanner-graphs with given symbol-node and check-node degrees and without small cycles. These graphs can be used to design high performance Low-Density Parity-Check (LDPC) codes. Our algorithm generates a graph by sequentially adding the edges to an empty graph. Recently, these types of sequential methods for counting and random generation have been very successful [35], [18], [11], [7], [4], [6].