Editing Rate–distortion theory (section)

== Connecting rate-distortion theory to channel capacity  ==
Suppose we want to transmit information about a source to the user with a distortion not exceeding ''D''. Rate–distortion theory tells us that at least <math>R(D)</math> bits/symbol of information from the source must reach the user. We also know from Shannon's channel coding theorem that if the source entropy is ''H'' bits/symbol, and the [[channel capacity]] is ''C'' (where <math>C < H</math>), then <math>H-C</math> bits/symbol will be lost when transmitting this information over the given channel. For the user to have any hope of reconstructing with a maximum distortion ''D'', we must impose the requirement that the information lost in transmission does not exceed the maximum tolerable loss of <math>H-R(D)</math> bits/symbol. This means that the channel capacity must be at least as large as <math>R(D)</math>.<ref name="BergerRateDistortion">{{cite book |title=Rate Distortion Theory: A Mathematical Basis for Data Compression |publisher=Prentice Hall |first=Toby |last=Berger |year=1971 |url=https://archive.org/details/ratedistortionth0000berg/ |url-access=registration |lccn=75-148254 |isbn=978-0-13-753103-5 |oclc=156968}}</ref>