Reduced wire-length and routing complexity for LDPC decoders

Random low-density parity-check (LDPC) codes have been shown to have better performance compared to structured codes because of their better minimum distance and girth. However, random codes result in decoders with large VLSI area and complex routing. The routing complexity is the main limitation for implementing practical fully parallel LDPC decoders. We use reordering sparse-matrix algorithms to reduce the average wire-length and congestion in fully parallel VLSI implementations. Rows and columns of the code matrix are rearranged such that each row/column connection is as close as possible. The restructuring achieves a 15% reduction in average wire-length and 30% in reducing the number of wires across an area. The shape of restructured code is predictable making it possible to develop better routing algorithms for such codes. The shape of the code also simplifies routing in that consecutive rows have almost the same range. Restructuring of the matrix does not change the code matrix and hence does not affect its performance.