Secure Coding for the Gaussian Wiretap Channel with Sparse Regression Codes

We consider the Gaussian wiretap channel (WTC), where two legitimate users communicate in the presence of a passive eavesdropper. Sparse Regression Codes (SPARCs) are capacity achieving codes for the AWGN and have been introduced by Joseph and Barron. In this paper, we draw parallels between standard wiretap encoding techniques,based on random binning, and the nested structure that exhibit and propose a coding scheme which achieves a level of information-theoretic security and reliability simultaneously. In particular, we consider SPARCs defined via an i.i.d. Gaussian dictionary as well as with a Bernoulli designed matrix and show that results are the same in both cases. Finally, we discuss how a concatenation with an outer code can be applied to our proposed secure encoding scheme and bound the probability of message error.