channel-capacity
Problem-solving strategies for channel capacity in information theory
npx skills add parcadei/Continuous-Claude-v3 --skill channel-capacity --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# 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 ```bash 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); p
- When to Use
- Decision Tree
- Tool Commands
- ScipyMutualInfo
- SympyBscCapacity
- Z3CapacityBound
- Key Techniques
- Cognitive Tools Reference
uv run python -m runtime.harness scripts/sympy_compute.py simplify "1 + p*log(p, 2) + (1-p)*log(1-p, 2)" uv run python -m runtime.harness scripts/z3_solve.py prove "I(X;Y) <= H(X)"
What does the channel-capacity skill do?
Problem-solving strategies for channel capacity in information theory
How do I install it?
Run `npx skills add parcadei/Continuous-Claude-v3 --skill channel-capacity --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From parcadei/Continuous-Claude-v3, a repository with 3,879 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.