We design staircase codes with overheads between 6.25% and 33.3% for high-speed optical transport networks. Using a reduced-complexity simulation of staircase coded transmission over the BSC, we select code candidates from within a limited parameter space. Software simulations of coded BSC transmission are performed with algebraic component code decoders. The net coding gain of the best code designs are competitive with the best known hard-decision decodable codes over the entire range of overheads. At 20% overhead, staircase codes are within 0.92 dB of BSC capacity at a bit error-rate of 10 −15. Decoding complexity and latency of the new staircase codes are also significantly reduced from existing hard-decision decodable schemes.

The speed at which two remote parties can exchange secret keys in continuous-variable quantum key distribution (CV-QKD) is currently limited by the computational complexity of key reconciliation. Multi-dimensional reconciliation using multi-edge lowdensity parity-check (LDPC) codes with low code rates and long block lengths has been shown to improve error-correction performance and extend the maximum reconciliation distance. We introduce a quasi-cyclic code construction for multi-edge codes that is highly suitable for hardware-accelerated decoding on a graphics processing unit (GPU). When combined with an 8dimensional reconciliation scheme, our LDPC decoder achieves an information throughput of 7.16 Kbit/s on a single NVIDIA GeForce GTX 1080 GPU, at a maximum distance of 142 km with a secret key rate of 6.64 × 10 −8 bits/pulse for a rate 0.02 code with block length of 10 6 bits. The LDPC codes presented in this work can be used to extend the previous maximum CV-QKD distance of 100 km to 142 km, while delivering up to 3.50× higher information throughput over the tight upper bound on secret key rate for a lossy channel.

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We analyze a class of high performance, low decoding-data-flow error-correcting codes suitable for high bit-rate optical-fiber communication systems. A spatially-coupled split-component ensemble is defined, generalizing from the most important codes of this class, staircase codes and braided block codes, and preserving a deterministic partitioning of component-code bits over code blocks. Our analysis focuses on low-complexity iterative algebraic decoding, which, for the binary erasure channel, is equivalent to a generalization of the peeling decoder. Using the differential equation method, we derive a vector recursion that tracks the expected residual graph evolution throughout the decoding process. The threshold of the recursion is found using potential function analysis. We generalize the analysis to mixture ensembles consisting of more than one type of component code, which provide increased flexibility of ensemble parameters and can improve performance. The analysis extends to the binary symmetric channel by assuming mis-correction-free component-code decoding. Simple upper-bounds on the number of errors correctable by the ensemble are derived. Finally, we analyze the threshold of spatially-coupled split-component ensembles under beyond bounded-distance component decoding.

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