Abstract
Quantum telecommunication has received a lot of attention today by providing unconditional security because of the inherent nature of quantum channels based on the no-cloning theorem. In this mode of communication, first, the key is sent through a quantum channel that is resistant to eavesdropping, and then secure communication is established using the exchanged key. Due to the inevitability of noise, the received key needs to be distilled. One of the vital steps in key distillation is named key reconciliation which corrects the occurred errors in the key. Different solutions have been presented for this issue, with different efficiency and success rate. One of the most notable works is LDPC decoding which has higher efficiency compared to the others, but unfortunately, this method does not work well in the codes with a high rate. In this paper, we present an approach to correct the errors in the high rate LDPC code-based reconciliation algorithm. The proposed algorithm utilizes Integer Linear Programming to model the error correction problem to an optimization problem and solve it. Testing the proposed approach through simulation, we show it has high efficiency in high rate LDPC codes as well as a higher success rate compared with the LDPC decoding method - belief propagation – in a reasonable time.
Highlights
Quantum key distribution protocols [1,2] share a secure key between two remote parties and establish secure communication between them using two channels; quantum channel and public channel
It is noteworthy that the (Mixed) (Integer) Linear programming approaches have already been used to decoding the Low-density parity check (LDPC) codes [22,23,24,25], but as it known, it is the first time that an Integer Linear Programming (ILP) model is utilized to reconcile the key in Quantum key distribution and key reconciliation algorithms
To evaluate the proposed ILP approach for error correction, we provide the detailed comparisons of the original Belief propagation algorithm (BP) algorithm, Multi-matrix BP (MBP) [8] and ILP proposed approach in different parameters; efficiency, success rate, and speed as three criteria for judging a key reconciliation algorithm
Summary
Quantum key distribution protocols [1,2] share a secure key between two remote parties and establish secure communication between them using two channels; quantum channel and public channel. In this paper, we decided to propose an approach to correct the errors in high rate codes. To do this we utilize Integer Linear Programming (ILP) approach. We present the detail of the proposed approach to correct errors in the sifted key based on the Integer Linear Programming approach. B can model the problem to an optimization problem aiming to find an error vector with minimum weight to satisfy equation (7) To do this, he defines variables, constraints, and objective function based on the nature of the original problem. The proposed ILP model for error correction problem is as follows:
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