Why can't we just add more signal levels?

Nyquist says the bit rate grows with log₂(L). So use a million levels. What stops us?

Bandwidth B 3000 Hz

Signal levels L 4

Each level carries log₂(L) bits.

Signal-to-noise ratio 20 dB

0 dB = noise as strong as the signal. 40 dB = a very clean line.

Nyquist bit rate2 × B × log₂(L)

Shannon capacityB × log₂(1 + SNR)

Most levels noise allowsL = √(1 + SNR)

Interactive demonstration: as signal levels increase, noise bands overlap and the receiver can no longer tell levels apart, which is why Shannon's capacity caps Nyquist's bit rate.