State-Dependent Gaussian Multiple Access Channels: New Outer Bounds and Capacity Results

Wei Yang, Yingbin Liang, Shlomo Shamai Shitz, H. Vincent Poor

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


This paper studies a two-user state-dependent Gaussian multiple-access channel (MAC) with state noncausally known at one encoder. Two scenarios are considered: 1) each user wishes to communicate an independent message to the common receiver; and 2) the two encoders send a common message to the receiver and the non-cognitive encoder (i.e., the encoder that does not know the state) sends an independent individual message (this model is also known as the MAC with degraded message sets). For both scenarios, new outer bounds on the capacity region are derived, which improve uniformly over the best known outer bounds. In the first scenario, the two corner points of the capacity region as well as the sum rate capacity are established, and it is shown that a single-letter solution is adequate to achieve both the corner points and the sum rate capacity. Furthermore, the full capacity region is characterized in situations in which the sum rate capacity is equal to the capacity of the helper problem. The proof exploits the optimal-transportation idea of Polyanskiy and Wu (which was used previously to establish an outer bound on the capacity region of the interference channel) and the worst case Gaussian noise result for the case in which the input and the noise are dependent.

Original languageEnglish (US)
Article number8362724
Pages (from-to)7866-7882
Number of pages17
JournalIEEE Transactions on Information Theory
Issue number12
StatePublished - Dec 2018

All Science Journal Classification (ASJC) codes

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


  • Channel with states
  • capacity region
  • dirty paper coding
  • multiple access channel
  • outer bound


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