Rateless Protograph LDPC Codes for Quantum Key Distribution

Abstract

Information reconciliation (IR) is a key step in quantum key distribution (QKD). In recent years, blind reconciliation based on low-density parity-check (LDPC) codes has replaced Cascade as a standard de facto since it guarantees efficient IR without a priori quantum bit error rate estimation and with limited interactivity between the parties, which is essential in high key-rate and long-distance QKD links. In this article, a novel blind reconciliation scheme based on rateless protograph LDPC codes is proposed. The rate adaptivity, essential for blind reconciliation, is obtained by progressively splitting LDPC check nodes, which ensures a number of degrees of freedom larger than puncturing in code design. The protograph nature of the LDPC codes allows us to use the same designed codes with a large variety of sifted-key lengths, enabling block length flexibility, which is important in largely varying key-rate link conditions. The code design is based on a new protograph discretized density evolution tool.