Hierarchical Polar Coding for Achieving Secrecy over Fading Wiretap Channels without any Instantaneous CSI

This paper presents a polar coding scheme to achieve secrecy in block fading binary symmetric wiretap channels without the knowledge of instantaneous channel state information (CSI) at the transmitter. For this model, a coding scheme that hierarchically utilizes polar codes is presented. In particular, on polarization of different binary symmetric channels over different fading blocks, each channel use is modeled as an appropriate binary erasure channel over fading blocks. Polar codes are constructed for both coding over channel uses for each fading block and coding over fading blocks for certain channel uses. In order to guarantee security, random bits are introduced at appropriate places to exhaust the observations of the eavesdropper. It is shown that this coding scheme, without instantaneous CSI at the transmitter, is secrecy capacity achieving for the simultaneous fading scenario. For the independent fading case, the capacity is achieved when the fading realizations for the eavesdropper channel is always degraded with respect to the receiver. For the remaining cases, the gap is analyzed by comparing lower and upper bounds. Remarkably, for the scenarios where the secrecy capacity is achieved, the results imply that instantaneous CSI does not increase the secrecy capacity. Index Terms Fading Channel, Information Theoretic Security, Polar Coding, Wiretap Channel. The material in this paper was presented in part at 2015 IEEE International Symposium on Information Theory (ISIT 2015), Hong Kong, June 2015. H. Si and S. Vishwanath are with the Laboratory for Informatics, Networks, and Communications, Wireless Networking and Communications Group, The University of Texas at Austin, Austin, TX 78712. O. O. Koyluoglu is with the Department of Electrical and Computer Engineering, The University of Arizona, Tucson, AZ 85721. Email: [email protected], [email protected], [email protected].