On the SNR-Evolution of the MMSE Function of Codes for the Gaussian Broadcast and Wiretap Channels

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

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


This paper considers the signal-to-noise ratio (SNR)-evolution, meaning the behavior as a function of the SNR, of the minimum mean-square error (MMSE) function of code sequences in several multi-user settings in the additive white Gaussian noise regime. The settings investigated in this context include the Gaussian wiretap channel, the Gaussian broadcast channel (BC), and the Gaussian BC with confidential messages (BCC). This paper shows that the specific properties of the SNR-evolution of the MMSE and conditional MMSE functions are necessary and sufficient conditions for capacity or equivocation achieving code sequences. In some cases, the complete SNR-evolution of a family of code sequences can be determined, providing significant insight into the disturbance (in terms of MMSE) such codes have on unintended receivers at other SNRs. Moreover, the effects of an additional MMSE constraint on the capacity region and on the SNR-evolution of code sequences are considered in the BC and BCC settings. Such an analysis emphasizes the tradeoff between rates and limited disturbance on unintended receivers.

Original languageEnglish (US)
Article number7407389
Pages (from-to)2070-2091
Number of pages22
JournalIEEE Transactions on Information Theory
Issue number4
StatePublished - Apr 2016

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


  • BCC
  • Gaussian channels
  • I-MMSE
  • MMSE constrained codes
  • SNR evolution
  • broadcast channels
  • multiuser channels
  • superposition codebooks
  • wiretap channels


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