On the design of multi-edge type LDPC codes and their applications to QKD systems

Abstract

In this work, we consider the design of multi-edge type low-density parity-check (MET-LDPC) code ensembles and their applications to quantum key distribution (QKD) systems. First, we propose a novel design rule of MET-LDPC code ensembles for capacity-approaching error-correcting performances. The proposed design rule efficiently sorts out invalid distributions in the design process, and does not assume any restriction on the search space. In addition, MET-LDPC codes are designed across a wide range of code rates on binary-erasure channel and binary-input additive-white Gaussian channel, which confirms that MET-LDPC codes with the proposed design rule have better threshold performances than existing codes with sets of limited code parameters. Secondly, this work studies the design of MET-LDPC code ensembles at low code rates with good threshold performances and an exponentially few number of small weight codewords. Degree-one variable nodes are indispensable in MET-LDPC code ensembles of low rates for achieving good threshold performances. However, the degree-one variable nodes may result in small weight codewords and thus must be carefully introduced to MET-LDPC code ensembles. This work derives the condition for an exponentially few number of small weight codewords in MET-LDPC code ensembles with degree-one variable nodes. The results allow us to design MET-LDPC code ensembles of low rates with both good threshold performances and exponentially few small weight codewords. Thirdly, as a consequence of two contributions, we propose a design rule of punctured MET-LDPC code ensembles for the continuous-variable QKD (CV-QKD) systems. The proposed design rule allows one to implement rate-compatible MET-LDPC codes with good performances both in the thresholds and low-error rate regions. It will be demonstrated that by employing the proposed rate-compatible MET-LDPC codes, the efficiency of information reconciliation (IR) for the CV-QKD systems can be significantly improved. The performance improvements are confirmed by comparing complexities and secret key rates of IR schemes with MET-LDPC codes whose ensembles are optimized with existing and the proposed design rules. Finally, this work proposes an efficient method to modify MET-LDPC code structure to have linear time encoding complexity. This work allows a linear-time encoding complexity without compromising their error-correcting performances, and the results make the applications of MET-LDPC codes practically viable.