Code design for type-I wiretap channel thanks

Ozarow and Wyner [1] proposed a secrecy code design scheme using a linear code and its cosets. It was shown that when a wiretap channel has a noiseless main channel and an eavesdropper taps a subset of coded bits through a wiretapper's channel, the eavesdroppers equivocation is readily, at least in theory, obtained by analyzing a parity-check matrix of the linear code. However, in general, the computational complexity to find the equivocation is prohibitively high and grows rapidly with the length of codewords. In order to avoid this problem, in this paper, we propose a tight lower bound on the equivocation that can be available by simple manipulations when a secrecy code is transmitted over a perfect-BEC type-I wiretap channel. The lower bound provides a guaranteed secrecy performance for various linear codes of any lengths for type-I perfect-BEC wiretap channel. Numerical results show that the lower bounds are sufficiently close to the equivocation. We also demonstrate how to use the lower bound to design secrecy codes for type-I wiretap channels with Gaussian main and wiretapper's channels.