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channel-capacity #

Visualizes a noisy channel as a probabilistic mapping p(y|x) (shown as a 2×2 transition matrix for a binary symmetric channel) and the channel capacity C as the maximum mutual information over input distributions: C = sup_{p(x)} I(X;Y). The lower plot animates I(X;Y) vs p(X=1) for the current noise level ε, highlighting the maximizing distribution and the capacity. A rate strip illustrates Shannon’s theorem: rates RC are not reliably achievable.

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practical uses #

• 01.Choosing modulation/coding rates that remain below channel capacity for reliable links
• 02.Understanding why increasing SNR (lower ε) increases maximum throughput
• 03.Designing/benchmarking error-correcting codes against theoretical limits

technical notes #

Implements a Binary Symmetric Channel (BSC) so p(y|x) is easy to display and capacity is C=1−H2(ε). Mutual information is computed as I=H2(P(Y=1))−H2(ε) with P(Y=1)=ε+q(1−2ε). Animations sweep ε and the input bias q; blocky rendering uses grid snapping and simple chunky glyphs on a green-on-black palette.

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