Optimization Design Of The Degraded Wiretap Channel With Polar Codes

Since it was proposed in2007, Polar code has been the hot topic in information theory for itscapacity-achieving property. By channel polarization, the bit-channels are divided into two parts,such as, noiseless bit-channels and pure noisy bit-channels. The construction of Polar code is tochoose the noiseless bit-channels as information transmitting channel, so as to improve thetransmission rate and ensure the reliability of the system. Wiretap channel is one typical model tostudy the secure communications at physical layer. In this thesis, we will focus on the application ofPolar code in wiretap channel..Firstly, the thesis studies the encryption optimization of the Polar code construction in thedegraded wiretap channel with the introduction of encryption and the Polar code construction indegraded wiretap channel. In the original scheme, the transmission rate of the system with Polarcode is close to the secure capacity, but is less than channel capacity of the main channel. The thesispresents a new construction scheme with encryption. In the scheme, the key is first transferred at thebit-channels good for Bob but bad for Eve. Then, the information is encrypted with the key, and istransmitted through the noiseless bit-channels of the main channel(Alice to Bob). At the receiver,Bob gets the information by decoding the ciphertext with the key, and Eve can not get anyinformation without the Key. The numerical simulation results show that when the SNR of the mainchannel is2dB, the transmission rate of the original scheme is0.2bit/Sys, the transmission rate ofthe new scheme is0.58bit/Sys; when the SNR of the main channel is9dB, the transmission rate ofthe original scheme is0.52bit/Sys, the transmission rate of the new scheme is0.89bit/Sys. The newscheme ensures the safety and the reliability of the system and improves the transmission rate.Next, the thesis studies the rate-compatible optimization design of Polar codes in the degradedwiretap channel. The different code rates should be used in different channel conditions for thewireless communication systems, which results in rate-compatible channel coding. The puncturingcode design is an effective way to achieve the rate-compatible channel code. The thesis furtherpresents the puncturing Polar code construction in the degraded wiretap channel. In the originalPolar codes construction scheme, the transmission rate is very low. By the proposed puncturingmatrix to the construction of Polar codes, a rate-compatible Polar code can be constructed. Thenumerical simulation results show that when the SNR of the main channel is2dB, the transmissionrate of the original scheme is0.2bit/Sys, the transmission rate of puncturing32bits scheme is 0.23bit/Sys, the transmission rate of puncturing64bits scheme is0.28bit/Sys. The new schemeachieves the rate-compatible Polar code and improves the transmission rate ensuring the safety andreliability of Polar code in the wiretap channel.