Channel Capacity
- 1 installs
- 3.9k repo stars
- Updated January 26, 2026
- parcadei/continuous-claude-v3
Guides Claude through information-theory channel-capacity problems using mutual information, channel matrices, and known channel capacities via scipy.
About
A decision-tree skill for computing channel capacity by maximizing mutual information over input distributions. A developer uses it when they want Claude to model channels like the binary symmetric channel and compute capacity.
- Mutual information via entropy decomposition
- Capacity formulas for standard channels like BSC
Channel Capacity by the numbers
- 1 all-time installs (skills.sh)
- Ranked #1,803 of 2,064 Data Science & ML skills by installs in the Skillselion catalog
- Data as of Aug 5, 2026 (Skillselion catalog sync)
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| Installs | 1 |
|---|---|
| repo stars | ★ 3.9k |
| Last updated | January 26, 2026 |
| Repository | parcadei/continuous-claude-v3 ↗ |
What it does
Guides Claude through information-theory channel-capacity problems using mutual information, channel matrices, and known channel capacities via scipy.
Files
Channel Capacity
When to Use
Use this skill when working on channel-capacity problems in information theory.
Decision Tree
1. Mutual Information
- I(X;Y) = H(X) + H(Y) - H(X,Y)
- I(X;Y) = H(X) - H(X|Y) = H(Y) - H(Y|X)
- Symmetric: I(X;Y) = I(Y;X)
scipy.stats.entropy(p) + scipy.stats.entropy(q) - joint_entropy
2. Channel Model
- Input X, output Y, channel P(Y|X)
- Channel matrix: rows = inputs, columns = outputs
- Element (i,j) = P(Y=j | X=i)
3. Channel Capacity
- C = max_{p(x)} I(X;Y)
- Maximize over input distribution
- Achieved by capacity-achieving distribution
4. Common Channels
| Channel | Capacity |
|---|---|
| Binary Symmetric (BSC) | 1 - H(p) where p = crossover prob |
| Binary Erasure (BEC) | 1 - epsilon where epsilon = erasure prob |
| AWGN | 0.5 * log2(1 + SNR) |
5. Blahut-Arimoto Algorithm
- Iterative algorithm to compute capacity
- Alternates between optimizing p(x) and p(y|x)
- Converges to capacity
z3_solve.py prove "capacity_upper_bound"
Tool Commands
Scipy_Mutual_Info
uv run python -c "from scipy.stats import entropy; p = [0.5, 0.5]; q = [0.6, 0.4]; H_X = entropy(p, base=2); H_Y = entropy(q, base=2); print('H(X)=', H_X, 'H(Y)=', H_Y)"Sympy_Bsc_Capacity
uv run python -m runtime.harness scripts/sympy_compute.py simplify "1 + p*log(p, 2) + (1-p)*log(1-p, 2)"Z3_Capacity_Bound
uv run python -m runtime.harness scripts/z3_solve.py prove "I(X;Y) <= H(X)"Key Techniques
From indexed textbooks:
- [Elements of Information Theory] Elements of Information Theory -- Thomas M_ Cover & Joy A_ Thomas -- 2_, Auflage, New York, NY, 2012 -- Wiley-Interscience -- 9780470303153 -- 2fcfe3e8a16b3aeefeaf9429fcf9a513 -- Anna’s Archive. Using a randomly generated code, Shannon showed that one can send information at any rate below the capacity C of the channel with an arbitrarily low probability of error. The idea of a randomly generated code is very unusual.
Cognitive Tools Reference
See .claude/skills/math-mode/SKILL.md for full tool documentation.
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