## 2 System Model and Problem Statement
### Problem Statement  
As mentioned in the Introduction, the NRK-SC scheme [15; 16; 17; 18] realizes secure communication using non-reconciled keys to deal with information leakage and the communication overhead caused by information reconciliation. For comparison purposes, we provide a brief description of the existing NRK-SC scheme [15; 16; 17; 18]. As shown in Figure 2, the non-reconciled keys \(K_{A}\) and \(K_{B}\) are generated by [PERSON] and [PERSON] via channel estimation and quantization. Note that since the inconsistent keys are not corrected via information reconciliation, channel coding is required to correct not only transmitted error bits but also inconsistent keys. After that, the generated keys \(K_{A}\) are used to encrypt encoded source bits \(X_{A}\) via exclusive-OR (XOR) encryption. Next, the ciphertexts \(E_{A}\) are transmitted to [PERSON] over the wireless channel. Then, [PERSON] receives the ciphertexts \(E_{B}\) and recovers \(X_{B}\) from the ciphertexts via XOR decryption. The source bits \(M_{B}\) can be obtained after channel decoding.  
In the XOR operation process, when the key and transmitted bit errors occur simultaneously, the errors can be corrected. As shown in Figure 2, note that \(E_{B}\) and \(K_{B}\) errors occur. The decrypted bit received by [PERSON] \(X_{B}=E_{B}\oplus K_{B}\) is correct. Thus, when there exists a channel correlation between key generation and secure transmission, the error probabilities of keys and transmitted bits are correlated, which can result in the achievement of an excellent error correction effect via the XOR operation. This is the potential advantage that channel correlation can offer.  
However, in the existing NRK-SC scheme, key generation and secure transmission are performed at different coherence times. The keys generated by the previous coherence time are used to encrypt the encoded data bits of the next coherence time. Thus, the error probability of keys is different from that of the transmitted bits, and the advantage does not apply. Moreover, non-reconciled keys share the error correction capability of channel coding in the NRK-SC scheme. Thus, more redundant code bits must be added to correct error bits, leading to a lower coding efficiency and a lower secure transmission  
Figure 1: System model.  
rate. Therefore, to address the problem and fully use the advantage of channel correlation, we propose a non-reconciled physical-layer keys-assisted secure communication scheme based on channel correlation.  
3 The Proposed Non-Reconciled Keys-Assisted Secure Communication Scheme Based on Channel Correlation  
As illustrated in Figure 3, the proposed scheme has three steps, namely, signal frame design, non-reconciled key generation, and secure transmission based on adaptive coding. The first step is aimed at designing the signal transmission process to fully use channel correlation between key generation and secure transmission. In the second step, the wireless channel is probed to generate non-reconciled keys. Subsequently, in the third step, the generated keys are used to encrypt encoded data bits to achieve secure transmission, where data source bits are encoded by the adaptive coding based on the equivalent channel. In the following, we discuss the three steps in detail.