Nested codes for secure transmission

Ruoheng Liu, H. Vincent Poor, Predrag Spasojevic, Yingbin Liang

Abstract: This paper investigates the problem of ensuring secure communication through error-correcting coding methods. A practical structured secure coding design is considered for a general wiretap channel, in which the main channel and the eavesdropper channel are binary-input symmetric-output memoryless (BISOM) channels. The proposed secure error-correcting code has a nested code structure. The nesting is based on cosets of a capacity-achieving sequence for binary erasure channels (BECs). The corresponding achievable secrecy rate is derived based on an erasure decomposition for the eavesdropper channel and an Bhattacharyya-equivalent channel construction for the main channel. Those two techniques allow a “degraded” erasure wiretap channel to be built and, hence, significantly simplify the practical coding design for secure transmission.