CCapacity Atlas
strong-interference-two-user-dmc

Two-user DMC in the strong-interference regime

Under the two strong-interference information inequalities, both receivers decode both messages and the capacity region is a MAC-region intersection.

Interference Finite alphabet Discrete memoryless Capacity region Exact Single-letter characterization

Channel and question

Input
Independent finite-alphabet inputs \(X_1\) and \(X_2\).
Output
Finite receiver outputs \(Y_1\) and \(Y_2\).
Law
A memoryless two-user interference channel satisfying the strong-interference inequalities for every product input law.
Quantity
Strong-interference capacity region \(\mathcal C_{\mathrm{SI}}\), measured in ordered pairs of bits per channel use.

Criterion. Closure of achievable independent-message rate pairs.

  • Transmitters carry independent private messages.
  • Average probability that either receiver errs vanishes.

Current status

\[\mathcal C_{\mathrm{SI}}=\mathcal C_{\mathrm{MAC},1}\cap\mathcal C_{\mathrm{MAC},2}\]

Conditions. The strong-interference inequalities hold for every product input distribution.

Known results and bounds for Two-user DMC in the strong-interference regime
ResultRelationMethodYear
Exact\(\mathcal C_{\mathrm{SI}}=\mathcal C_{\mathrm{MAC},1}\cap\mathcal C_{\mathrm{MAC},2}\)Both receivers decode both messages without a rate penalty.1975

Formal verification

Lean coverageFormally stated

New statements await mathematical review and proofs.

Claims

  • The strong-interference region uses the same time-sharing law at both receivers.
    operational-capacity · exact capacity · solved · Formally stated · v1
Lean declarations (3)

References

  1. A. B. Carleial (1975). A Case Where Interference Does Not Reduce Capacity. IEEE Transactions on Information Theory. DOI 10.1109/TIT.1975.1055352.
  2. Te Sun Han and Kingo Kobayashi (1981). A New Achievable Rate Region for the Interference Channel. IEEE Transactions on Information Theory. DOI 10.1109/TIT.1981.1056307.

Discussion

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