Designing LDPC codes using bit-filling

Bipartite graphs of bit nodes and parity check nodes arise as Tanner graphs corresponding to low density parity check codes. Given graph parameters such as the number of check nodes, the maximum check-degree, the bit-degree, and the girth, we consider the problem of constructing bipartite graphs with the largest number of bit nodes, that is, the highest rate. We propose a simple-to-implement heuristic BIT-FILLING algorithm for this problem. As a benchmark, our algorithm yields codes better or comparable to those in MacKay [1].