Channel capacity (Shannon limit)

Channel capacity is the speed limit of the universe for information: the absolute maximum rate, in bits per second, at which you can send data over a channel with arbitrarily few errors. Claude Shannon proved in 1948 that this ceiling depends on just two things — how much bandwidth B you have and how clean your signal is (the SNR) — captured in the elegant Shannon–Hartley formula C = B·log2(1 + SNR). Below this rate, clever coding can drive errors essentially to zero; above it, no scheme on Earth can keep them down.

The formula carries deep lessons. Because capacity grows only with the *logarithm* of SNR, doubling your transmit power buys little extra speed — but it grows *linearly* with bandwidth, so getting more spectrum is far more powerful. This is exactly why 5G hungers for wide millimetre-wave bands and why Wi-Fi keeps widening its channels. Shannon's result also birthed the entire field of error-correcting codes, by promising that reliable communication near the limit was possible — turning a hunt for impossible perfection into an engineering race toward a known finish line.