Source Coding Theory

WAV unpacks to FLAC and back bit-for-bit: redundancy removed, real sound untouched.

What it is

Source coding is squeezing audio to the smallest honest size by removing redundancy, not real sound.

Key facts

• Shannon's Source Coding Theorem (1948): you CANNOT compress below the source entropy H without losing data, period
• Entropy formula: H = -Σ p(i) log2 p(i), where p(i) = probability of symbol i, log2 = log base 2, H = average bits needed per symbol
• Lossless = bit-exact, unzips to the IDENTICAL file (every sample, zero loss); lossy = throws data away, never comes back
• CD-quality WAV (PCM): 44.1 kHz sample rate, 16-bit depth, 2 channels = 1,411 kbps = ~10.1 MB per stereo minute
• Lossless FLAC/ALAC typically shrink WAV to 50-60% (about a 2:1 ratio) with ZERO quality loss
• Lossy MP3 at 320 kbps is ~4.4:1 smaller than WAV; 128 kbps is ~11:1 smaller
• Redundancy = predictable/repeated data; entropy coding (Huffman, arithmetic, Rice/Golomb) packs frequent values into fewer bits
• Nyquist theorem: sample rate must be >= 2x the highest frequency; 44.1 kHz captures up to ~22.05 kHz (human hearing tops ~20 kHz)
• Bit depth sets dynamic range: ~6.02 dB per bit, so 16-bit = ~96 dB, 24-bit = ~144 dB of range
• Lossy codecs use a psychoacoustic model: they bin sounds the ear cannot hear (masking) - that is perceptual coding, NOT pure source coding

How it works

1. Read the raw audio stream (PCM samples) coming off the file
2. Predict each sample from the ones before it - silence and tones are highly predictable
3. Store only the small prediction ERROR, not the full value (this is the clever packing)
4. Entropy-code those errors: frequent small values get short bit codes, rare big ones get long codes
5. Wrap it in a container (FLAC/ALAC) with headers so a decoder can rebuild it
6. Decode = run the maths backwards to get the EXACT original samples back

Real examples

• A 5-minute stereo WAV (~50 MB) saved as FLAC drops to ~25-30 MB, still bit-perfect for the show
• Emailing a band their multitrack stems as FLAC instead of WAV halves the upload time
• A silent intro or sustained pad compresses heavily because it is so predictable (low entropy)
• White noise or a dense full mix barely compresses - it is near-random, high entropy, little redundancy to remove
• Archiving a festival's recorded sets: FLAC saves ~half the drive space with no audible or measurable loss

How it helps in live sound

• Archive show recordings and stems as FLAC (lossless) - half the storage, zero quality loss for re-mixing later
• Send mastered tracks to clients as FLAC or 24-bit WAV, never lossy, so they keep full headroom
• Run virtual soundcheck files and backing tracks as WAV/FLAC on the desk - never MP3, decode artefacts can glitch
• For walk-in/background playback off a phone, 320 kbps AAC/MP3 is fine and saves space
• Keep your master archive lossless; only make lossy copies for casual streaming or quick previews
• Label sample rate + bit depth on every file (e.g. 48k/24-bit) so the system clocks correctly and avoids resampling