On Gaussian wiretap channels with M-PAM inputs

Miguel R.D. Rodrigues, Anelia Somekh-Baruch, Matthieu Bloch

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

18 Scopus citations


This paper investigates the secrecy capacity of the Gaussian wiretap channel with M-PAM inputs, by capitalizing on the relationship between mutual information and minimum mean squared error (MMSE). In particular, we establish optimality conditions for both the M-PAM input power and the M-PAM input distribution, which we specialize to the asymptotic low-power and high-power regimes. By using the properties of the MMSE to establish sufficient conditions for the uniqueness of the solution of some of the underlying non-convex optimization problems, we also propose efficient algorithms to compute the optimal solutions. Interestingly, we show that with M-PAM inputs it is sub-optimal to use all the available power for some range of parameters - this is in sharp contrast to standard Gaussian channels. We also extend the results to the parallel Gaussian wiretap channel with M-PAM inputs. We put forth a mercury-waterfilling interpretation of the optimal power allocation procedure for parallel Gaussian wiretap channels which generalizes the conventional mercury-waterfilling interpretation for parallel Gaussian channels, with the mercury level amending the base level to account for both the non-Gaussianess of the input and the secrecy constraint.

Original languageEnglish
Title of host publication2010 European Wireless Conference, EW 2010
Number of pages8
StatePublished - 2010
Event2010 European Wireless Conference, EW 2010 - Lucca, Italy
Duration: 12 Apr 201015 Apr 2010

Publication series

Name2010 European Wireless Conference, EW 2010


Conference2010 European Wireless Conference, EW 2010


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