## 1 Introduction  
With the continuous evolution of wireless communication technology, ubiquitous mobile communication has become an indispensable part of our daily life. In particular, fifth-generation (5G) wireless communications transmit a large amount of information with high data rates and extremely low latency, which further promotes the rapid development of the Internet of Things (IoT) [1; 2; 3; 4]. Meanwhile, information security is always the main concern in wireless communications because the open and broadcast nature of the wireless medium leads to inherent vulnerability to eavesdropping attacks. Thus, considerable research focuses on classic public-key cryptography techniques to ensure the confidentiality of transmitted information [5]. However, public-key infrastructure is required to be established in these techniques, which leads to difficulties in key distribution and management in resource-limited communication systems. In addition, these techniques rely on the computational complexity of mathematical problems and are thus at risk of being broken by powerful quantum computers in the foreseeable future [6]. Recently, the physical-layer key generation technique, which is considered a supplement to upper-layer public key cryptography techniques, has attracted widespread attention [7; 8]. As a secure approach to key distribution and management based on the wireless channel, this technique can exploit the characteristics of the wireless channel to generate random keys from the wireless channel. Specifically, based on the reciprocity and temporal variation of the wireless channel, two legitimate users can extract unpredictable and highly correlated channel state information (CSI) after probing channels. Moreover, the spatial decorrelation of the wireless channel prevents eavesdroppers from obtaining the relevant information of the legitimate channels, to ensure the security of keys generated by legitimate users [9]. The physical-layer key generation consists of four steps, i.e., channel estimation, quantization, information reconciliation, and privacy amplification [10]. In general, the channel estimates of two legitimate users are inconsistent due to channel fading and noise. Thus, to generate identical symmetric keys, information reconciliation is required by sending signals to correct channel estimation errors between two legitimate users. There are several common information reconciliation methods such as cascade [11] and BBBSS [12]. In order to improve reconciliation efficiency, the authors in [13] designed a new hybrid information reconciliation protocol. The reconciled keys are used to encrypt transmitted data information to achieve secure transmission, which can be termed a reconciled physical-layer keys-based secure communication (RK-SC) scheme [14]. However, the reconciliation signals are sent over the public channel, which increases the communication overhead and the risk of eavesdropping attacks. Therefore, increasing attention is being directed at integrated schemes such as physical-layer secure communication schemes using non-reconciled keys. Note that an integrated non-reconciled physical-layer keys-based secure communication (NRK-SC) scheme was first proposed in [15]. This scheme generates keys without information reconciliation but shares the error correction capability of channel coding. Based on [15], the authors in [16] designed an efficient polar code that could significantly improve the secure communication efficiency of the NRK-SC scheme. Moreover, the authors in [17] evaluated the superior performance of the NRK-SC scheme compared to the RK-SC scheme by deriving the bit error ratio (BER), channel capacity, and security capacity. Similarly, it was proved that the NRK-SC scheme outperformed the RK-SC scheme in terms of communication overhead, computation complexity, and the secure transmission rate in [18]. However, note that the existing NRK-SC scheme no longer corrects inconsistent keys via information reconciliation but instead adds key errors to the transmission process.