Study On Wiretap Channel Using Polar Code

Polar code is so far the only kind of channel coding scheme which can achieve the Shannon limit in theory with low complexity encoding and decoding algorithm. By channel polarization, communication channel can be polarized into pure noisy bit-channels and noiseless bit-channels. Information bits are designed to be transmitted only in the noiseless bit-channels by the construction of polar code, which will lead to the the highest information transmission rate. This thesis will focus on the research of the degraded wiretap channel and the general non-degraded wiretap channel using polar code.The wiretap model proposed by Wyner is an important model of physical layer for the research of security, where the channel between legitimate users (Sender Alice and receiver Bob) is called the main channel and the channel between eavesdropper and Alice is called eavesdropping channel. Generally, the eavesdropping channel is assumed to have bigger noise than that of the main channel. In this thesis, we first analyze the safety encoding scheme with polar code based on the degraded wiretap channel model, and then we address an improved encoding scheme by combining the construction of polar code with encryption algorithm. The numerical simulation results show that the security transmit rate can be improved in case that the degradation degree is limited.Furthermore, we study the safety encoding method on non-degraded wiretap channel model (that the noise in the main channel is the same as that one in the eavesdropping channel) using polar code. We first evolute the non-degraded BSC wiretap channel model to degraded one by two-way communication method, then we present the equivalent parameter of the degraded wiretap channel model. By theoretical calculation and numerical simulation, we find the security capacity of the non-degraded BSC wiretap channel model with the safety encoding method of polar code in above discussion. Similarly, we study the non-degraded Gaussian wiretap channel model and propose a corresponding polar encoding scheme for it.