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IEEE Information Theory Workshop (ITW)

LDPC-based Gaussian key reconciliation

Matthieu R. Bloch, Andrew Thangaraj, S.W. McLaughlin, Jean-Marc Mérolla

Published May 25, 2006• 64 citations
Publisher

Abstract

We propose a new information reconciliation method which allows two parties sharing continuous random variables to agree on a common bit string. We show that existing coded modulation techniques can be adapted for reconciliation and give an explicit code construction based on LDPC codes in the case of Gaussian variables. Simulations show that our method achieves higher efficiency than previously reported results.

DOI
10.1109/itw.2006.1633793

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We propose a new information reconciliation method which allows two parties sharing continuous random variables to agree on a common bit string. We show that existing coded modulation techniques can be adapted for reconciliation and give an explicit code construction based on LDPC codes in the case of Gaussian variables. Simulations show that our method achieves higher efficiency than previously reported results.
This paper investigates an efficient and practical information reconciliation method in the case where two parties have access to correlated continuous random variables. We show that reconciliation is a special case of channel coding and that existing coded modulation techniques can be adapted for reconciliation. We describe an explicit reconciliation method based on LDPC codes in the case of correlated Gaussian variables. We believe that the proposed method can improve the efficiency of quantum key distribution protocols based on continuous-spectrum quantum states.
This paper investigates a practical secret key agreement protocol over the Gaussian wire-tap channel. The protocol is based on an efficient information reconciliation method which allows two parties having access to correlated continuous random variables to agree on a common bit string. We describe an explicit reconciliation method based on LDPC codes optimized with EXIT charts and density evolution. When used in conjunction with existing privacy amplification techniques our method allows secret key agreement over the Gaussian wire-tap channel close to the secrecy capacity
An information reconciliation method for continuous-variable quantum key distribution with Gaussian modulation that is based on non-binary low-density parity-check (LDPC) codes is presented. Sets of regular and irregular LDPC codes with different code rates over the Galois fields GF(8)GF(8)GF(8), GF(16)GF(16)GF(16), GF(32)GF(32)GF(32), and GF(64)GF(64)GF(64) have been constructed. We have performed simulations to analyze the efficiency and the frame error rate using the sum-product algorithm. The proposed method achieves an efficiency between 0.940.940.94 and 0.980.980.98 if the signal-to-noise ratio is between 444 dB and 242424 dB.
Abstract Quantum key distribution (QKD) is the most mature application of quantum information technology. Information reconciliation is a crucial step in QKD and significantly affects the final secret key rates shared between two legitimate parties. We analyze and compare various construction methods of low-density parity-check (LDPC) codes and design high-performance irregular LDPC codes with a block length of 10 6 . Starting from these good codes and exploiting the slice reconciliation technique based on multilevel coding and multistage decoding, we realize high-efficiency Gaussian key reconciliation with efficiency higher than 95% for signal-to-noise ratios above 1. Our demonstrated method can be readily applied in continuous variable QKD.
Information reconciliation is a significant step for a continuous-variable quantum key distribution (CV-QKD) system. We propose a reconciliation method that allows two authorized parties to extract a consistent and secure binary key in a CV-QKD protocol, which is based on Gaussian-modulated coherent states and homodyne detection. This method named spherical reconciliation is based on spherical quantization and non-binary low-density parity-check (LDPC) codes. With the suitable signal-to-noise ratio (SNR) and code rate of non-binary LDPC codes, spherical reconciliation algorithm has a high efficiency and can extend the transmission distance of CV-QKD.
Reconciliation is an essential part of any secret-key agreement protocol and hence of a quantum key distribution (QKD) protocol, where two legitimate parties are given correlated data and want to agree on a common string in the presence of an adversary, while revealing a minimum amount of information. In this paper, we show that for discrete-variable QKD protocols, this problem can be advantageously solved with low density parity check (LDPC) codes optimized for the binary symmetric channel (BSC). In particular, we demonstrate that our method leads to a significant improvement of the achievable secret key rate, with respect to earlier interactive reconciliation methods used in QKD.