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I · Information theory

Channel capacity (Shannon-Hartley)

What it is

C = B · log₂(1 + S/N). Bits per second for a noisy channel of bandwidth B and signal-to-noise S/N.

Where it lives

Why a 25 MHz Wi-Fi channel can't carry 10 Gbit. The hard ceiling on every modulation scheme.

The key insight

Linear in bandwidth, logarithmic in SNR. Doubling power gives one extra bit per symbol.

More in Information theory

Shannon entropy H(X) = −Σ p(x) log₂ p(x). The expected number of bits needed to encode… Mutual information I(X;Y) = H(X) − H(X∣Y). How much knowing Y reduces uncertainty about X… KL divergence D_KL(P‖Q) = Σ p(x) log(p(x)/q(x)). The "extra bits" cost of using Q to…

Across the foundations

II Concentration inequalities Probability & randomness II Bayes theorem Probability & randomness III Shortest paths Graph theory III Min-cut / Max-flow Graph theory III Spanning trees Graph theory III Connectivity & cycles Graph theory IV Little's law Queueing theory IV M/M/1 queue Queueing theory

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