The Puzzle
Analog Voice
Raw PCM
"If digital needs 4× more bandwidth, why would anyone use it?"
Claude Shannon's Answer
1948 — "A Mathematical Theory of Communication"
Shannon proved that any channel has a maximum capacity for reliable communication — and showed how to approach it.
Compression
Remove redundancy from the source. Speech is predictable — exploit that!
Error Correction
Add strategic redundancy back. Detect and fix transmission errors.
Together: Digital can be both efficient AND reliable
Digital Advantages
Regeneration
Signal restored perfectly at each repeater — no noise accumulation
Analog
Digital
Signal quality after 8 repeater hops
Perfect Copies
No generation loss — copy of a copy is identical to original
Original
→
Copy 10
100%
→
Copy 100
100%
Compression
Modern codecs use less bandwidth than analog!
Raw PCM
Analog
Modern
Error Correction
Detect and fix transmission errors automatically
Transmitted
1
0
0
1
1
0
↓ corrected
1
0
1
1
1
0
Recovered
Flexibility
Once it's bits, you can do anything with it
🔐 Encrypt
📊 Multiplex
💾 Store
🔀 Route
⚙️ Process
🔍 Search
📡 Broadcast
🌐 Network
Honest Tradeoffs
Quantization Noise
Some information is always lost when converting to discrete levels
Smooth curve → discrete steps = some loss
Latency
Encoding and decoding take time
Encode
→
Transmit
→
Decode
Cliff Effect
Works perfectly... until it suddenly doesn't
Analog
Graceful degradation
Digital
Sudden failure