## 4 Simulation and Results
Specifically, at the observed QBER of 0.25, the syndrome-based estimation with \(N=\) 64,800 and \(N_{sb}=\) 16,200 bits achieves mean accuracies of 95.1979% and 95.1631%, respectively. However, if the estimated value of QBER exceeds 11% [32] or cannot be determined within \(q_{threshold}\), the set of sifted keys from this post-processing cycle must be aborted to ensure information-theoretic security in the QKD system. For implementation, the proposed syndrome-based estimation, employing \(N=\) 64,800 bits and \(R_{C}^{(max)}=\) 9/10, is appropriate for the primary round. Meanwhile, \(N_{sb}=\) 16,200 bits with \(R_{C}^{(max)}=\) 8/9 can be utilized in the occasional additional rounds. To analyze the efficiency of the proposed rate-adaptive reconciliation integrated with syndrome-based QBER estimation and subblock confirmation, the number of information leakages during the information reconciliation step (\(L_{rec}\)) is considered to evaluate the efficiency metric of information reconciliation (\(\eta_{IR}\)). According to Equation (6), \(\eta_{IR}\) can be reformulated in terms of \(L_{rec}\), expressed as follows:  
\[\eta_{IR}=\frac{L_{rec}}{H(q_{est})\cdot N}, \tag{23}\]  
where \(N\) represents the sifted key size. For the proposed scheme, the number of information leakages is quantified by the total amount of syndrome information that _[PERSON]_ transmits to _[PERSON]_ during the syndrome-based estimation and rate-adaptive reconciliation steps, which consists of two parts. Firstly, it includes the syndrome information derived from the primary round, which handles the full size of the sifted key at \(N=\) 64,800 bits for the LDPC's block length. The second part consists of the syndrome information generated during the additional rounds, which were conducted specifically in response to failures in the subblock confirmation step. Each of these unsuccessful subblocks was processed using the specific LDPC codes with block lengths of \(N_{sb}=\) 16,200 bits for syndrome-based estimation and rate-adaptive reconciliation. Therefore, the information leakages of the proposed scheme (\(L_{rec}\)) can be formulated by:  
\[L_{rec}=\bigg{[}M_{R_{C}^{(max)}}+\ \ (R_{C}^{(max)}-R_{C}^{(opt)})\cdot N \bigg{]}\ +\ \sum_{i=1}^{m_{fail}}\bigg{[}M_{s_{b_{i}},\ R_{C}^{(max)}}+\ \ (R_{C,\ sh}^{(max)}-R_{C,\ sh}^{(opt)})\cdot N_{sb} \bigg{]}. \tag{24}\]  
In Equation (24),\(M_{R_{C}^{(max)}}\) represents the number of check nodes in the parity-check matrix \(\mathbf{H}_{R_{C}^{(max)}}\) associated with the maximum code rate \(R_{C}^{(max)}\) for syndrome-based estimation. Additionally, \(R_{C}^{(opt)}\) denotes the calculated optimal coding rate based on the number of puncturing bits \(n_{p}\) and shortening bits \(n_{s}\) for rate-adaptive reconciliation used in the primary round, as detailed in Equations (14)-(16). Meanwhile, the unverified subblocks from \(i\) to \(m_{fail}\) are processed in the additional rounds. In this context, \(M_{s_{b_{i}},\ R_{C}^{(max)}}\) denotes the number of check nodes in \(\mathbf{H}_{R_{C}^{(max)}}\) associated with subblock lengths \(N_{sb}\) of \(R_{C,\ sh_{b}}^{(max)}\), which is used for syndrome-based estimation; the calculated optimal coding rate \(R_{C,\ sh_{b}}^{(opt)}\) is used for rate-adaptive reconciliation. In the case of a successful confirmation within the primary round, \(L_{rec}\) relies exclusively on the syndrome information obtained from the primary round. Consequently, additional rounds become unnecessary, and \(m_{fail}=\) 0. In Figure 6, the performance of the proposed rate-adaptive reconciliation, integrated with syndrome-based QBER estimation and subblock confirmation, is compared against the existing methods. These methods include Cascade with a frame length of \(10^{4}\) bits [12], blind reconciliation using LDPC codes with a block length of \(10^{4}\) bits [18], and symmetric blind reconciliation with LDPC block lengths of 4 \(\times\)\(10^{3}\) bits [20].