We present an optical low-density parity-check (LDPC) decoder suitable for implementation above 100 Gbits/s, which provides large coding gains when based on large-girth LDPC codes. We show that a basic building block, the probabilities multiplier circuit, can be implemented using a Mach–Zehnder interferometer, and we propose corresponding probabilistic-domain sum-product algorithm (SPA). We perform simulations of a fully parallel implementation employing girth-10 LDPC codes and proposed SPA. The girth-10 LDPC(24015,19212) code of the rate of 0.8 outperforms the turbo-product code of the rate of 0.82 by 0.91 dB (for binary phase-shift keying at 100 Gbits/s and a bit error rate of ), and provides a net effective coding gain of 10.09 dB.
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