channel-capacity
Provides mathematical strategies for solving channel capacity problems.
Install
mkdir -p .claude/skills/channel-capacity && curl -L -o skill.zip "https://agentskills.codes/api/skills/download/6841" && unzip -o skill.zip -d .claude/skills/channel-capacity && rm skill.zipInstalls to .claude/skills/channel-capacity
Activation
This is the description your AI agent reads to decide when to run this skill — the better it matches your request, the more reliably it fires.
Problem-solving strategies for channel capacity in information theoryKey capabilities
- →Calculate mutual information using Scipy
- →Compute channel capacity for BSC and BEC models
- →Verify information theory bounds using Z3
- →Simplify capacity expressions with Sympy
How it works
It utilizes Scipy for entropy calculations, Sympy for symbolic simplification, and Z3 for proving bounds on channel capacity.
Inputs & outputs
When to use channel-capacity
- →Calculate mutual information
- →Compute channel capacity for BSC/BEC
- →Verify bounds using Z3
About this skill
Channel 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.
When not to use it
- →When the problem falls outside information theory models
Limitations
- →Limited to supported channel models like BSC, BEC, and AWGN
How it compares
It automates the application of specific information theory algorithms like Blahut-Arimoto instead of manual derivation.
Compared to similar skills
channel-capacity side by side with the closest alternatives in the catalog.
| Skill | Installs | Updated | Safety | Difficulty |
|---|---|---|---|---|
| channel-capacity (this skill) | 1 | 7mo | Review | Advanced |
| literature-review | 559 | 2mo | Review | Advanced |
| openalex-database | 48 | 7mo | Review | Intermediate |
| scientific-critical-thinking | 18 | 7mo | Review | Advanced |
Try saying
Example prompts that trigger this skill in your AI assistant.
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