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A forward-error correction (FEC) scheme based on low-density parity check (LDPC) codes and iterative decoding using belief propagation in code graphs is presented in this paper. We show that LDPC codes provide a significant system performance improvement with respect to the state-of-the-art FEC schemes employed in optical communications systems. We present a class of structured codes based on mutually orthogonal Latin rectangles. Such codes have high rates and can lend themselves to very low-complexity encoder/decoder implementations. The system performance is further improved by a code design that eliminates short cycles in a graph employed in iterative decoding.