Multilevel LDPC-Coded High-Speed Optical Systems: Efficient Hard Decoding and Code Optimization

We consider a multilevel coding scheme employing low-density parity-check (LDPC) codes and high-order modulations for high-speed optical transmissions, where the coherent receiver performs either parallel independent decoding (PID) or multistage decoding (MSD). To meet the severe complexity constraint imposed by the ultrahigh data rate of the emerging optical transmission systems, we focus on hard-decision decoding of LDPC codes. A new LDPC hard decoding method is developed, which is equivalent to the Gallager decoding algorithm B, but is more efficient in terms of circuit implementation, since no variable node degree information is needed. Two variants of this decoder is also proposed, which offers significant performance gain for finite-length codes. We optimize the system by allocating rates and designing profiles for component codes. Both numerical evaluations and simulation results show that the optimized multilevel coding systems with either PID or MSD substantially outperform the optimized single-level LDPC-coded system.