Rate distortion theory is the part of information theory that answers: How many bits are minimally needed to represent a source if we allow some distortion? It is the lossy-compression counterpart of entropy/source coding theory.
For lossless compression, the fundamental limit is the entropy ; for lossy compression, the fundamental limit is the rate-distortion function , where number of bits per source symbol, allowed average distortion, and represents minimum achievable rate under distortion level .