Shannon Information Theory

It is the basic science of how any message, including audio, can be measured, sent down a wire, and rebuilt at the other end without getting wrecked.

A mic signal becomes bits, crosses a noisy channel, and is rebuilt error-free at the other end.

What it is

The basic science of measuring any message in bits, sending it down a noisy wire, and rebuilding it perfectly at the other end.

Key facts

Founder: Claude Shannon, 1948 paper 'A Mathematical Theory of Communication' at Bell Labs - the birth of the digital age.
The BIT (binary digit) is the unit of information: one yes/no choice, 2 possible states.
Channel Capacity formula C = B x log2(1 + S/N): C = max error-free bits/second, B = bandwidth in Hz, S/N = signal-to-noise power ratio.
Shannon's Noisy Channel Coding Theorem: below capacity C you can transmit with error as close to zero as you want; above C, errors are guaranteed.
Nyquist-Shannon Sampling Theorem: to capture a signal perfectly, sample at 2x the highest frequency. Human hearing tops ~20 kHz, so audio samples at 44.1 kHz (CD) or 48 kHz (pro/video).
Bit depth sets dynamic range: ~6.02 dB per bit. 16-bit = ~96 dB, 24-bit = ~144 dB of range before noise/clipping.
Entropy H = average information per symbol, measured in bits; high entropy = unpredictable = more bits to send.
Redundancy is what lets error correction work: add extra check bits so the receiver can detect and fix flips.
Two coding jobs are separate: SOURCE coding (compress, remove redundancy, e.g. MP3/FLAC) and CHANNEL coding (add redundancy back to beat noise, e.g. Dante/RF).
More bandwidth B raises capacity linearly; more S/N raises it only logarithmically - so a cleaner signal helps, but a wider pipe helps more.

How it works

Measure the message: count how much real information (entropy, in bits) it carries.
Source-code it: compress to strip redundant data and shrink the file (MP3, FLAC, AAC).
Channel-code it: add controlled redundancy / error-correction bits so noise can be undone.
Send it down the channel, which has a hard speed limit C set by bandwidth and signal-to-noise.
Receiver detects and corrects any flipped bits using the redundancy, then rebuilds the original.
Decode back to audio - identical to the source if you stayed under capacity C.

Real examples

A wireless mic encoding a vocal into a digital RF stream that survives interference and decodes clean at the receiver.
A 48 kHz / 24-bit stagebox sending 64 channels down one Cat5e Dante cable instead of 64 analogue snakes.
Streaming a gig: the show is compressed (source coding), wrapped in error correction (channel coding), then rebuilt on a phone.
A CD: 44.1 kHz / 16-bit, with Reed-Solomon error correction so scratches still play perfectly.
MP3/AAC throwing away inaudible data (lossy source coding) to shrink a track to ~10% of WAV size.

How it helps in live sound

Run digital snakes (Dante/AVB) on shielded Cat5e/Cat6 under 100 m - keep S/N high so the link sits well under capacity and never drops audio.
Set pro recording/desks to 48 kHz; that captures the full ~20 kHz audible band with Nyquist headroom (24 kHz limit).
Record at 24-bit for ~144 dB range - huge headroom means quiet passages stay above the noise floor and you won't clip.
Coordinate wireless mic frequencies and keep RF S/N strong; weak S/N drops you below capacity and you get dropouts/digital nasties.
On streams, give the encoder enough upload bitrate (bandwidth) - starving B forces lossy artefacts on the audience.
Don't sample-rate convert needlessly; every conversion risks aliasing and dither noise - pick one rate (48 kHz) for the whole rig.

Everyday analogy

It is the post office for sound: every signal gets packed into countable parcels (bits), shipped down a noisy road, and rebuilt perfectly at the far end.

Watch out

Myth: 'higher sample rate / more bits always sounds better.' Truth: past Nyquist (48 kHz covers all of human hearing) and 24-bit (144 dB), you're just storing data your ears and gear can't use - clean gain staging and S/N matter far more.

Fun fact

Shannon's MIT master's thesis (showing electrical switches can do Boolean logic) has been called the most important master's thesis of the 20th century - it is literally why digital computers exist.

Key takeaways

Everything digital - mics, desks, Dante, streaming - is built on Shannon's 1948 maths.
Information is counted in bits; a channel has a hard speed limit C = B x log2(1 + S/N).
Sample at 2x the top frequency (Nyquist) or you get aliasing - junk frequencies.
Stay under capacity C and you can hit basically zero errors; go over and errors are unavoidable.
Redundancy isn't waste - it's the spare parts that let the receiver fix damage.
Compression removes redundancy; error correction adds it back - opposite jobs, both needed.