Channel and question
- Input
- Each terminal chooses an element of a common finite abelian group.
- Output
- Terminal one sees X1+X2+Z1 and terminal two sees X1+X2+Z2.
- Law
- Group addition with independent memoryless noises having arbitrary fixed group distributions.
- Quantity
- Modulo-additive two-way channel capacity \(\mathcal C\), measured in bits per channel use.
Criterion. Vanishing average block error, with the constraints specified in the model.
- The two messages are independent and uniform.
- Each encoder knows its own message and strictly past local outputs.
- Each decoder knows its own message and its entire local output word.
- R1 is the rate from terminal one to terminal two, and R2 is the reverse rate.
Current status
\[0\le R_1\le\log_2|G|-H(Z_2),\quad 0\le R_2\le\log_2|G|-H(Z_1)\]
| Result | Relation | Method | Year |
|---|---|---|---|
| Exact | \(0\le R_1\le\log_2|G|-H(Z_2),\quad 0\le R_2\le\log_2|G|-H(Z_1)\) | Self-input cancellation and conditional-entropy converses. | 2016 |
Formal verification
Lean coverageFormally stated
Concrete operational definitions and admitted research statements are present. Existing proofs are preserved. New statements require mathematical review and proof completion.
Claims
- Independent memoryless additive noises give a rectangular capacity region even with adaptation.
operational-capacity· exact capacity · solved · Formally stated · v1
Lean declarations (1)
CapacityAtlas.Claims.additiveTwoWayclaim · operational-capacity
lean/CapacityAtlas/Claims/AdditiveTwoWay.lean — Independent memoryless additive noises give a rectangular capacity region even with adaptation.
References
- Lin Song, Fady Alajaji, and Tamas Linder (2016). Adaptation is Useless for Two Discrete Additive-Noise Two-Way Channels. IEEE International Symposium on Information Theory.