Secure communications is one of the key challenges faced in the field of information security as the transmission of information between legitimate users is vulnerable to interception by illegitimate listeners. The state-of-the -art secure communication schemes employ cryptographic encryption methods. However, the use of cryptographic encryption methods requires generation, distribution and management of keys to encrypt the confidential message. Recently, physical layer security schemes that exploit the difference between the channel conditions of the legitimate users and the illegitimate listeners have been proposed for enhanced communication security. We propose novel coding schemes for secure transmission of messages over compound channels that provides another level of security in the physical layer on top of the existing cryptographic security mechanisms in the application layer. Our aim is to provide secrecy against illegitimate listeners while still offering good communication performance for legitimate users. We consider the transmission of messages over compound channels, where there are multiple parallel communication links between the legitimate users and an illegitimate listener intercepts one of the communication links that is unknown to the legitimate users. We propose a special source splitter structure and a new family of low density parity check code ensembles to achieve secure communications against an illegitimate listener and provide error correction capability for the legitimate listener. First, the source bit sequence is split into multiple bit sequences by using a source splitter. The source splitter is required to make sure that the illegitimate listener does not have access to the secret message bits directly. Then, a special error correction code is applied to the bit sequences, which are the outputs of the source splitter. The error correction code is based on a special parity check matrix which is composed of some subblocks with specific degree distributions. We show that the proposed communication schemes can provide algebraic and information theoretic security. Algebraic security means that the illegitimate listener is unable to solve any of the individual binary bits of the secret message. Furthermore, information theoretic security guarantees the highest level of secrecy by revealing no information to the illegitimate listener about the secret message. The error correction encoder produces multiple codewords to be sent on parallel links. Having access to the noisy outputs of the parallel links, the legitimate receiver recovers the secret message. The finite length performance analysis of the proposed secure communications scheme for the legitimate listener shows good results in terms of the bit error rate and the frame error over binary input additive white Gaussian noise channel. The asymptotic performance analysis of our scheme for a sufficiently large block length is found via the density evolution equations. Since the proposed low density parity check code is a multi-edge type code on graphs, there are two densities that characterize the system performance. The thresholds obtained by the density evolution equations of our scheme show comparable or improved results when compared to the fully random low density parity check codes.


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