Design of nested protograph-based LDPC codes with low error-floors

In this paper, we propose a method to design nested protograph-based low-density parity-check (LDPC) codes for network communications with low error-floors via a graph modification procedure. Lowering the error-floor of nested LDPC codes is essential for certain applications that require very low decoded error rates in moderate to high signal-to-noise-ratios (SNRs) like optical communication and data storage. The multilevel method we propose improves upon existing state-of-the-art algebraic designs by the identification and removal of harmful graph structures from nested LDPC codes, effectively improving the performance of each of the nested codes in their error-floor region. Simulation results are provided that confirm the expected performance improvement.