# High Efficiency Continuous-Variable Quantum Key Distribution Based on ATSC 3.0 LDPC Codes
## 1 Introduction  
Quantum key distribution (QKD) [1; 2; 3] is one of the most pragmatic applications of quantum communication technologies. QKD enables two remote parties named [PERSON] and [PERSON] to extract a symmetrical string of secret keys via a quantum channel, even in the presence of an eavesdropper, and promises unconditional security in principle [4]. Currently, there are two types of protocol, including discrete variable (DV) QKD [5] and continuous-variable (CV) QKD [6; 7; 8]. In DVQKD, the polarization or phase of weak coherent states is used as the carrier of information and the quantum states received are measured by using a single-photon detector. In continuous-variable quantum key distribution (CVQKD), the amplitudes and phase quadratures of Gaussian-modulated coherent states are considered to be the carriers of information and the receiver utilizes homodyne or heterodyne detection techniques to measure the transmitted quantum states [9]. For a CVQKD system based on Gaussian-modulated coherent states, future-proof security against collective attacks has been provided. Furthermore, such detectors used in CVQKD systems are routinely deployed in classical optical communications; hence, the CVQKD system offers very good prospects for implementations based on mature telecom components [4]. Generally, the quantum communication link and the information postprocessing are two parts of the CVQKD system [10; 11]. In the quantum communication link part, the quantum states are prepared on [PERSON]'s side and then sent to [PERSON] via a quantum channel. Then, [PERSON] performs a measurement onquantum states by using a homodyne detector. In the information postprocessing part, both [PERSON]'s side and [PERSON]'s side process the information and get symmetrical secret keys through correcting errors. Technically, the reconciliation efficiency is one of major factors limiting the secret key rate and the transmission distance of a CVQKD system [12]. Therefore, a high reconciliation efficiency is necessary to realize a high secret key rate and long transmission distance. The ideal secret key rate \(K_{ideal}\) is given by  
\[K_{ideal}=\beta I_{AB}-\chi_{BE}, \tag{1}\]  
where the reconciliation efficiency is measured by \(\beta=R/C(s)\), \(R\) is the adopted rate of low-density parity-check (LDPC) codes and \(C(s)\) is the channel capacity at signal-to-noise ratio (SNR) value \(s\). \(I_{AB}\) denotes the mutual information between [PERSON] and [PERSON]. The maximum of the [PERSON] information leaked to [PERSON] is denoted by \(\chi_{BE}\). However, secret key rate \(K\) in Equation (1) is the maximum achievable value without considering reconciliation frame error rate (FER). Taking the reconciliation FER into account, the final secret key rate of the CVQKD system is given by [13; 14]  
\[K_{final}=(1-\text{FER})(\beta I_{AB}-\chi_{BE}). \tag{2}\]  
It can be clearly seen from Equation (2) that for a given FER, in order to obtain a high secret key rate, the reconciliation efficiency should be as large as possible. Therefore, researchers begin to discover more efficient error-correcting codes to improve reconciliation efficiency. An expansion operation is proposed in [15], which provides a way to use quasi-cyclic (QC)-LDPC codes in the 5G protocol for information reconciliation and achieves high efficiency above 0.926 at rate 22/68. In [13; 16; 17], repeat accumulate (RA) LDPC codes, multi-edge type (MET) LDPC codes and punctured LDPC codes are adopted in the information reconciliation of the CVQKD system respectively. Generally, for a given LDPC code, low SNR is required to achieve high reconciliation efficiency \(\beta\). Compared with the LDPC codes mentioned above, Advanced Television Systems Committee (ATSC) LDPC codes can require a lower SNR under the same FER and code rate \(R\), which means that a lower channel capacity and a higher reconciliation efficiency can be obtained by applying ATSC LDPC codes to the CVQKD system.