The Study Of The Optimal Feedback Coding Schemes For The Gaussian Wiretap Channels

With the rapid development of electronic technology,communication technology and computer technology,the security of communication systems is indispensable.These technologies are widely used in military,telecommunications and other sectors.The communication channel model is generally composed of three parts,the sender,receiver,and Eavesdropper,which constitute the original model of the wiretap channel.In this paper,we study the Gaussian wiretap feedback channel.Exploring the three coding and decoding schemes,we obtain the optimal coding schemes on degraded and non-degraded models.Firstly,we studied the secret key based feedback scheme was proposed by Ahlswede-Cai,which focuses on generating a key from the feedback and using the key as part of transmitted message.Next,we studied a new hybrid feedback coding scheme by Dai,which is not only used to generate keys,but also generate auxiliary information help legitimate receivers improve the Communication.In addition,we studied SK scheme because of the scheme shows excellent performance in Gaussian channels.As we all known,noiseless feedback cannot increase the security capacity of the channel,but it can significantly reduce the coding work,use feedback to reduce the complexity and delay the coding and decoding process.Finally,we applied the three schemes to the degraded and non-degraded conditions of the Gaussian wiretap feedback channels,and obtained the following conclusions.Under the degraded Gaussian wiretap feedback channel,the hybrid feedback scheme proposed by Dai is simplified to the key-based feedback scheme,neither of them can achieve the security capacity,while the SK scheme can reach the security capacity without privacy constraints,so under the degraded model,the SK coding scheme is optimal.Under the non-degenerate Gaussian wiretap feedback channel,our research shows that the hybrid coding feedback scheme performs as well as the SK scheme,and both of them can reach the security capacity without privacy constraints,but the secret key based feedback scheme still cannot reach the security capacity,under the non-degenerate model,the hybrid scheme and SK scheme are excellent,both of them are better than the key-based feedback scheme.In order to make our research more realistic,we designed a secure coding and decoding scheme for Gaussian wrietap channel by Hamming code,which through a series of processes such as encoding,modulation,demodulation and decoding.Then the conclusion shows that our scheme is effective.