Secrecy Capacity of Colored Gaussian Noise Channels with Feedback

Chong Li, Yingbin Liang, H. Vincent Poor, Shlomo Shamai

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


—In this paper, the finite-order autoregressive moving average (ARMA) Gaussian wiretap channel with noiseless causal feedback is considered, in which an eavesdropper receives noisy observations of signals in both forward and feedback channels. It is shown that the generalized Schalkwijk-Kailath scheme, a capacity-achieving coding scheme for the feedback Gaussian channel, achieves the same maximum rate for the same channel even with the presence of an eavesdropper. Therefore, the secrecy capacity is equal to the feedback capacity without the presence of an eavesdropper for the feedback Gaussian channel. Furthermore, the results are extended to the additive white Gaussian noise (AWGN) channel with quantized feedback. It is shown that the proposed coding scheme achieves a positive secrecy rate. Our result implies that as the amplitude of the quantization noise decreases to zero, the secrecy rate converges to the capacity of the AWGN channel.

Original languageEnglish (US)
Pages (from-to)5771-5782
Number of pages12
JournalIEEE Transactions on Information Theory
Issue number9
StatePublished - 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


  • Colored Gaussian
  • Feedback
  • Schalkwijk-Kailath Scheme
  • Secrecy Capacity


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