Rate-Distortion Theory

R(D) = max(0, ½ log₂(σ²/D)) for a Gaussian source. Explore the tradeoff between compression rate and distortion, and see where real compression schemes operate.

Source variance σ² 16.0

Operating distortion D 4.0

16.0

σ² (variance)

4.0

Distortion D

1.00

Rate R(D) bits/sym

6.0

Source SNR (dB)

R(D) curve PCM (uncompressed) JPEG-like lossy MP3-like audio Operating point

R(D) = max(0, ½ log₂(σ²/D)) — Gaussian source, squared-error distortion

Points below the R(D) curve are unachievable. All lossless compression operates on the vertical axis (D=0). Rate-distortion theory gives the theoretical minimum rate for any given distortion.