| Very powerful long low-density parity-check (LDPC) codes, such as the ITU G.975.1 Standard (32643, 30592) LDPC Code [1], have been considered for optical communications. Traditional implementations of such long codes result in circuits requiring millions of interconnections, which are not affordable. This thesis investigates the performance of the hard-decision differential decoding with binary message-passing (DD-BMP) algorithm [2], a low-complexity algorithm requiring a minimal number of wires due to its binary messages. Our simulation results for the ITU G.975.1 standard demonstrate that hard-decision DD-BMP algorithm outperforms the results provided in the standard, and that the gap between the decoding performance of hard-decision DD-BMP and hard-decision sum-product is small at high signal-to-noise ratios (SNR). We also present a novel design methodology for implementing a soft-decision decoder by exploiting the code's structure. An implementation-efficient architecture is presented using a partially-parallel adaptation of the min-sum algorithm known as the line-passing algorithm. The line-passing algorithm makes soft-decision decoding available while requiring a minimal number of interconnections, which is attractive for long-haul optical communication systems. |
