Cooperative jamming polar codes for multiple-access wiretap channels

The authors study cooperative security in the physical layer of wireless systems based on the recently developed polar codes for multiple access channel (MAC). Specifically, the authors first consider the case of a m-user MAC with external eavesdropper. Using polar alignment, the authors formulate a discrete optimisation problem where security and reliability criteria can be handled separately over the bases of a set of deterministic binary matrices. A discrete algorithm with incrementally polynomial complexity is used to maximise the uniform sum secrecy rate of users. Moreover, the proposed coding scheme is shown to achieve strong security for any subset of users. The authors next examine the case of minimum number of cooperative helpers to fulfil a feasible secrecy rate requirement at the legitimate user. Here, a low-complexity suboptimal algorithm is presented with at most one helper more than the optimal solution. Using Tal-Sharov-Vardy implementation of MAC polar codes, secure polar coding is implemented for a 2-user Gaussian wiretap MAC channel. The upper and lower bound of block error probability are compared, respectively, at the legitimate receiver and the eavesdropper. The results demonstrate clearly that with sufficiently long block length, strong secrecy with respect to the eavesdropper is achieved, while block error probability approaches 0.5.