Low rate protograph-based LDPC codes for continuous variable quantum key distribution

Error correction plays a major role in the reconciliation of continuous variable quantum key distribution (CV-QKD) and greatly affects the performance of the system. CV-QKD requires error correction codes of extremely low rates and high reconciliation efficiencies. There are only very few code designs available in this ultra low rate regime. In this paper, we introduce a method for designing protograph-based ultra low rate LDPC codes using differential evolution. By proposing type-based protographs, a new way of representing low rate protograph-based LDPC codes, we drastically reduce the complexity of the protograph optimization, which enables us to quickly design codes over a wide range of rates. We show that the codes resulting from our optimization outperform the codes from the literature both in regards to the threshold and in finite-length performance, validated by Monte-Carlo simulations, showing gains in the regime relevant for CV-QKD.