On MMSE properties of optimal codes for the Gaussian wiretap channel

Ronit Bustin, Rafael F. Schaefer, H. Vincent Poor, Shlomo Shitz Shamai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations


This work examines the properties of "good" codes for the scalar Gaussian wiretap channel that achieve the maximum level of equivocation. Specifically, the minimum mean-square error (MMSE) behavior of these codes is explored as a function of the signal-to-noise ratio (SNR). It is first shown that reliable decoding of the codeword at the legitimate receiver and at the eavesdropper, conditioned on the transmitted message, is a necessary and sufficient condition for an optimally secure code sequence. Moreover, it is observed that a stochastic encoder is required for any code sequence with rate below the channel point-to-point capacity. Then, for code sequences attaining the maximum level of equivocation, it is shown that their codebook sequences must resemble "good" point-to-point, capacity achieving, code sequences. Finally, it is shown that the mapping over such "good" codebook sequences that produces a maximum equivocation code must saturate the eavesdropper. These results support several "rules of thumb" in the design of capacity achieving codes for the Gaussian wiretap.

Original languageEnglish (US)
Title of host publication2015 IEEE Information Theory Workshop, ITW 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781479955268
StatePublished - Jun 24 2015
Event2015 IEEE Information Theory Workshop, ITW 2015 - Jerusalem, Israel
Duration: Apr 26 2015May 1 2015

Publication series

Name2015 IEEE Information Theory Workshop, ITW 2015


Other2015 IEEE Information Theory Workshop, ITW 2015

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering
  • Computer Networks and Communications
  • Information Systems
  • Computational Theory and Mathematics


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