Research On Secrecy Coding Using Polar Codes

The issue of wireless communication security has drawn much attention alongside the exponential development of wireless communication technology.Unlike traditional cryptographic means,physical-layer security(PLS)technology emerges as a new paradigm to enhance wireless communication security based on information theory,making full use of the built-in features of wireless channels to ensure the secrecy of information.Secrecy coding is the key technique of PLS at the coding level,and currently,designing specific,lowcomplexity secrecy coding scheme for wireless networks is a major challenge of this field.Polar codes are the first class of provable capacity-achieving codes with low encoding/decoding complexity,and have already been adopted by the fifth generation(5G)of mobile networks.Polar codes are naturally bound to the channel characteristics based on the channel polarization phenomenon,which fits well with the fundamental idea of PLS.Therefore,it is of great importance to investigate secrecy polar coding for future wireless communication systems.This dissertation focuses on theoretical research and design of secrecy polar coding for typical wiretap channels and source-type models for key generation in PLS field.The detailed contributions are summarized as follows.(1)Polar coding design for the wiretap channel with shared key(WTC-K):For WTC-K where key encryption is combined with wiretap channel coding,a polar coding scheme,which achieves its secrecy capacity under the strong secrecy condition,is proposed.The proposed scheme is mainly built on the superposition coding structure and the polar coding design for general wiretap channels,which can fully integrate the secrecy capability of both key encryption and wiretap channel coding.The proposed scheme adopts the chaining construction mechanism without any symmetry or degradation assumptions on the wiretap channel.The reliability and strong secrecy of the proposed scheme are demonstrated by a theoretical evaluation.An example of a binary erasure wiretap channel with shared key is also given,and the performance bounds of the scheme are analyzed and verified numerically.(2)Polar coding design for the multiple access channel with confidential messages(MAC-CM):For MAC-CM under the scenario of mutual eavesdropping between users,a polar coding scheme,which achieves its achievable secrecy rate region under the strong secrecy condition,is proposed.The proposed scheme is mainly based on Arikan’s monotone chain expansion method and the polar coding design for general wiretap channels,with consideration of the self-interference problem of users in full-duplex mode.The proposed scheme adopts the chain construction mechanism without any symmetry or degradation assumptions on MAC-CM.The reliability and strong secrecy of the proposed scheme are demonstrated by a theoretical evaluation.An example of a binary erasure multiple access channel with confidential messages is also given,and the performance bounds of the scheme are analyzed and verified numerically.(3)Polar coding design for the three-terminal source-type model for key generation:For the three-terminal source-type model,two scenarios,namely rate-unlimited and rate-limited public channel are considered respectively,and two polar coding schemes,which achieve the achievable key rate of this model under the strong secrecy condition,are proposed.Unlike traditional schemes that guarantee reliability and secrecy via information reconciliation and privacy amplification means separately,the polar coding scheme features an alternative approach that jointly deal with reliability and secrecy in the form of secrecy codes.The proposed scheme is implemented by one-way communication between legitimate users,and only a portion of random bits with negligible rate is required to be shared among legitimate users.The proposed scheme adopts a bidirectional chaining construction mechanism without any symmetry or degradation assumptions on correlated sources.The reliability and strong secrecy of the proposed scheme are demonstrated by a theoretical evaluation.An example of a three-terminal binary symmetric source model for key generation is also given,and the performance bounds of the scheme are analyzed and verified numerically.(4)Polar coding design for the joint source-channel model:For the joint source-channel model which embraces both correlated sources and the wiretap channel,a polar coding scheme,which achieves the tradeoff between the rates of secret message and secret key under the strong secrecy condition,is proposed.The proposed scheme mainly consists of two parts,one for source coding and the other for channel coding,to realize key generation from correlated sources and secure transmission over the wiretap channel,respectively.The proposed scheme is a non-trivial combination and extension of the polar coding scheme of the source-type model for key generation with rate-limited public channel and that of WTC-K.The proposed scheme adopts the chain construction mechanism without any assumption of symmetry or degradation on both correlated sources and the wiretap channel.The reliability and strong secrecy of the proposed scheme are demonstrated by a theoretical evaluation.An example of a joint binary erasure source-channel model is also given,and the performance bounds of the scheme are analyzed and verified numerically.In summary,this dissertation focuses on the research of secrecy polar coding and develops four polar coding schemes that achieve the secrecy capability of corresponding PLS models under the strong secrecy condition,respectively.The proposed schemes serve to complement and enrich the current research on secrecy polar coding,and can accordingly provide theoretical guidance for the application and deployment of PLS in future wireless networks.