## 1 Introduction
An alternative protocol is Winnow [13], which employs the syndrome from a Hamming code, a type of forward error correction, to reconcile errors in a set of sifted keys while requiring less interactive communication. However, its performance is constrained by the error-correction capabilities of the Hamming code. Additionally, other forward error correction applications, such as Bose-Chaudhuri-Hocquenghem (BCH) [14; 15] and low-density parity-check (LDPC) [16; 17] codes, have been proposed for the information reconciliation protocol by selecting the appropriate channel coding rates based on a priori QBER estimation. By utilizing irregular LDPC codes and syndrome decoding based on the belief propagation algorithm, the interactive blind reconciliation method [18] can operate without a priori estimation of QBER. This approach relies on interactive communications and continues the reconciliation process until successful decoding is achieved. The technique of blind reconciliation was further adapted with variable step sizes [19] and transformed into a symmetric operation [20], potentially improving efficiency and reducing the required interactivity. Considering the importance of channel error estimation, the accuracy of a priori error estimation significantly influences the performance of information reconciliation based on LDPC codes. In particular, the value of the estimated QBER is crucial for choosing the optimal LDPC coding rate, which can improve blind reconciliation scenarios by reducing the necessity for additional interactive communications. In [21], the QBER value was estimated using the syndrome information from LDPC codes within a rate-adaptive reconciliation scheme. This syndrome-based QBER estimation approach was further extended in [22] by employing irregular LDPC codes with punctured or shortened bits. Furthermore,the multiple syndrome information obtained from multi-LDPC codes was proposed for error estimation and information reconciliation [23]. In [24], an asymmetric approach to rate-adaptive and blind reconciliation was proposed with a priori error rate estimation based on the exponential moving average of QBER from the previously corrected frames. Generally, information reconciliation schemes based on LDPC codes cannot always guarantee the exact identity of the reconciled keys due to potential failures in LDPC decoding. These failures can be caused by several factors, such as an insufficient number of iterations during decoding or an inaccurate QBER estimation. Therefore, a confirmation step is necessary to verify the identical key between the two parties. In [25], a confirmation method using a universal hash function was combined with the blind reconciliation. However, this method discards subblocks with mismatched hash values, ensuring only verified identical keys progress to the subsequent step. Despite considerable progress in information reconciliation based on LDPC codes, most existing methodologies primarily focus on simulations, either as standalone processes [17; 18; 19; 20] or in combination with channel error estimation [21; 22; 23; 24]. To further advance this work, a unified approach is investigated by integrating three main effective algorithms for error estimation, information reconciliation, and confirmation steps. Firstly, the syndrome information generated from the maximum code rate of irregular LDPC codes is employed to determine the QBER value, leveraging the maximum likelihood estimator to cover the potential errors in a QKD system. Then, the estimated QBER value is utilized to the rate-adaptive reconciliation scheme to optimize the appropriate channel coding rate of irregular LDPC codes through puncturing and shortening techniques. Finally, the subblock confirmation using hash verification is seamlessly incorporated with the rate-adaptive reconciliation. This step divides the reconciled keys into subblocks and verifies their identities with a polynomial-based hash function [26].