Channel Capacity Theorem

It is the hard speed limit on how much information you can reliably push through any link, like a cable, radio, or stream, before errors creep in.

Wide clean pipe = high capacity C; bits flow safely below C, but cram past it and the link drops out.

What it is

The hard, provable speed limit on how much data any link can carry error-free, set by its bandwidth and how clean the signal is versus the noise.

Key facts

Shannon-Hartley formula: C = B x log2(1 + S/N) — C is max error-free bits per second, B is bandwidth in hertz, S is signal power, N is noise power.
Push your data rate above C and errors are guaranteed; stay below C and near-zero errors are achievable.
S/N is the signal-to-noise RATIO as a plain power ratio, NOT decibels. Convert dB to ratio: 10^(dB/10), so 30 dB SNR = a ratio of 1000.
Wider pipe scales fast: doubling bandwidth B roughly doubles capacity C. Cleaner pipe helps slowly: capacity grows with the LOG of SNR.
Each extra 3 dB of SNR adds only about 1 bit/s per hertz of theoretical capacity; in real radios a practical ~6 dB extra is the rule of thumb to add one bit per symbol while holding the error rate.
+3 dB = double power, +10 dB = 10x power, -3 dB = half power.
Named after Claude Shannon, 1948 paper 'A Mathematical Theory of Communication' — the birth of information theory.
Below the Shannon limit, error-correction coding gives arbitrarily reliable transmission; above it, no code can fix it.
Bit = 1 binary digit; 8 bits = 1 byte; 1 kbps = 1000 bits/second. Lower the noise floor N and capacity climbs.
Speed of sound approximately 343 m/s at 20 C — the acoustic delay you budget on TOP of the data-link capacity, not the link limit itself.

How it works

Measure the bandwidth B (hertz) the link gives you — the width of the pipe.
Measure signal power S and noise power N, or read SNR straight off the receiver.
Convert SNR from dB to a plain ratio: 10^(dB/10).
Plug into C = B x log2(1 + S/N) to get the max safe bits per second.
Set your actual data rate (channel count, bitrate, resolution) safely BELOW C.
Need more? Widen B or raise SNR (stronger signal, lower noise), then recompute.

Real examples

A wireless mic at the back of a venue drops out: distance and walls cut S, noise N stays, SNR collapses, capacity falls below the audio bitrate.
Adding more digital wireless channels works until you run out of clean spectrum (B) — then they fight and glitch.
Dante/AVB audio over clean Cat6 carries dozens of channels; a damaged or too-long run raises errors and drops packets.
A live stream auto-drops from 1080p to 480p when wifi SNR falls — the encoder backs off below the shrinking capacity.
Long unbalanced analogue snake near dimmers picks up hum: more N, worse SNR, less usable headroom.

How it helps in live sound

Keep wireless mic receivers in LINE OF SIGHT and in range so SNR stays high; directional paddle antennas raise S without raising N.
Run a coordinated frequency plan so each mic gets clean bandwidth B; gaps between channels stop intermod glitches.
Use shielded correct-length Cat6/Cat6A for Dante/AVB; under 100 m per run keeps errors near zero.
Scan with an RF analyser to see the noise floor N; give wireless and IEMs their own clean space.
On a stream, set bitrate below real upload capacity with margin and let adaptive bitrate ride the link down — don't force HD over weak wifi.
Lower noise at the source: balanced lines, away from dimmers/LED walls/motors — every dB of SNR is more headroom.

Everyday analogy

It is a motorway with a fixed number of lanes: only so many cars fit per minute, and cramming in more just causes crashes instead of moving more traffic.

Watch out

Myth: 'just crank the transmitter or push more channels and it'll get through.' Wrong — past capacity C you get MORE dropouts, not more signal, and raising SNR only helps by the log, so doubling power adds barely a bit per hertz.

Fun fact

Shannon proved in 1948 that error-free comms is possible right up to the limit even over a noisy channel — but only that it CAN be done, not how; engineers took 50 years to invent codes (turbo, LDPC) that crept within a fraction of a dB of his limit.

Key takeaways

Every link has a hard ceiling C = B x log2(1 + S/N) in bits/second.
Width (bandwidth) scales capacity fast; cleanliness (SNR) only by the logarithm.
Below C you can be near-perfect; above C errors are mathematically guaranteed.
Weak or noisy wireless drops out because falling SNR drags capacity under the audio rate.
To send more safely: widen the pipe or lower the noise, not just crank power.