Channel Capacity Skill for Claude
Problem-solving strategies for channel capacity in information theory
Install
one command, takes just this skill from the repositorynpx skills add https://github.com/parcadei/Continuous-Claude-v3 --skill channel-capacityThe instruction itself
9 sections, as written by the authorChannel Capacity
When to Use
Use this skill when working on channel-capacity problems in information theory.
Decision Tree
- 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
- Channel Model
- Input X, output Y, channel P(Y|X)
- Channel matrix: rows = inputs, columns = outputs
- Element (i,j) = P(Y=j | X=i)
- Channel Capacity
- C = max_{p(x)} I(X;Y)
- Maximize over input distribution
- Achieved by capacity-achieving distribution
- 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) |
- 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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How to use it
Take parcadei/channel-capacity from the repository into ~/.claude/skills for personal
use, or into .claude/skills inside a project.
The agent identifies a skill by the name field in its header. Two skills with the
same name cannot sit side by side — one of them will be ignored.