[#P3106] Exact capacity region of the two-user Gaussian interference channel
Problem. Determine the exact capacity region of the memoryless real two-user Gaussian interference channel \(Y_1=X_1+aX_2+Z_1\) and \(Y_2=bX_1+X_2+Z_2\) for arbitrary fixed \(a,b\in\mathbb R\), independent standard Gaussian noises, and average power constraints \(\mathbb E[X_i^2]\le P_i\).
1Context
Known frontier: The Han-Kobayashi scheme with modern analysis achieves rates within one bit of capacity universally; several parameter regimes are exact. Open boundary: A matching exact capacity region for arbitrary gains and powers remains unknown.
2Problem setup
Definition 1 (capacity region). All rate pairs achievable by block codes with error tending to zero.
Definition 2 (interference channel). Each receiver observes its intended signal plus the other sender's signal and noise.
Remark 1. The capacity region is the closure of simultaneously achievable rate pairs with vanishing error. Exact formulas are known in strong and several other regimes; the general weak and mixed regimes are known within a constant gap.
3What counts as a solution
- Give matching single-letter or computable inner and outer bounds for all parameters a,b,P₁,P₂.
- Or prove that no proposed finite-letter characterization can hold under a precisely stated formulation and replace it with an exact operational characterization.
1Status
Current status (Current status and exact unresolved remainder). OPEN as checked on 2026-08-01. Strongest checked neighboring result: The Han-Kobayashi scheme with modern analysis achieves rates within one bit of capacity universally; several parameter regimes are exact. Exact unresolved remainder: A matching exact capacity region for arbitrary gains and powers remains unknown.[1][2]
1Records
Notes and companion material
Original intake status. OPEN as checked on 2026-08-01. Strongest checked neighboring result: The Han-Kobayashi scheme with modern analysis achieves rates within one bit of capacity universally; several parameter regimes are exact. Exact unresolved remainder: A matching exact capacity region for arbitrary gains and powers remains unknown.
- Equivalent-formulation queries: general two user Gaussian interference channel exact capacity remains open 2026; Gaussian interference channel capacity within one bit exact region
- Strongest checked neighboring result: The Han-Kobayashi scheme with modern analysis achieves rates within one bit of capacity universally; several parameter regimes are exact.
- Exact unresolved remainder: A matching exact capacity region for arbitrary gains and powers remains unknown.
How the 4 records connect
ProblemExact capacity region of the two-user Gaussian interference channel
2See also
- Capacity of the general discrete memoryless relay channelinformation theory
- Optimal balanced-subset Mastermind on twelve pointsinformation theory
- A 368-word code in the fifth strong power of the 7-cycleinformation theory
How to cite
TheoremDB contributors, “Exact capacity region of the two-user Gaussian interference channel,” TheoremDB research memory, snapshot of August 1, 2026. https://theoremdb.org/statements/gaussian-interference-channel-capacityThis page as plain text: gaussian-interference-channel-capacity.md
This problem includes 4 records joined by 3 typed links, sourced from arxiv.org[1], current as of August 1, 2026.
1References
- Packet source. R. Etkin, D. Tse, and H. Wang, Gaussian interference channel capacity to within one bit, IEEE Transactions on Information Theory 54 (2008). main one-bit theorem. ↗preprint · primary source · arXiv:cs/0702045, checked 2026-08-01 · checked 2026-08-01Source use: original summary.Approximates the full capacity region to within one bit for all parameters while stating exact capacity remains open.Also cited at R. Etkin, D. Tse, and H. Wang, Gaussian interference channel capacity to within one bit, IEEE Transactions on Information Theory 54 (2008). main one-bit theorem.Source used to assess the problem's recorded status.For Exact capacity region of the two-user Gaussian interference channel: This is the dated publication status for the canonical target Exact capacity region of the two-user Gaussian interference channel.Source named by the research packet.
- Te Han and K. Kobayashi, “A new achievable rate region for the interference channel”. IEEE Transactions on Information Theory 27(1) (1981), 49-60. DOI 10.1109/TIT.1981.1056307. Han-Kobayashi region. ↗journal article · primary source · checked 2026-08-01Source use: original summary.Provides the central achievable region against which converses are compared.Source used to assess the problem's recorded status.For Exact capacity region of the two-user Gaussian interference channel: Provides the central achievable region against which converses are compared.
Original TheoremDB editorial statement and source synthesis; external works are used for citation only.