Intradependent encodings can be compressed

Given an en­cod­ing scheme \(E\) which gives an In­trade­pen­dent en­cod­ing of a mes­sage \(m,\) we can in prin­ci­ple de­sign a more effi­cient cod­ing \(E^\prime\) that gives a shorter en­cod­ing of \(m.\) For ex­am­ple, \(E\) en­codes 8-let­ter English words as a se­ries of let­ters, \(m\) is aard­vark, then \(E(m)\) is in­trade­pen­dent (be­cause you already know what the mes­sage is by the time you’ve seen “aardv”), so you can define an al­ter­na­tive en­cod­ing \(E^\prime\) which en­codes “aard­vark” as just “aardv”, thereby sav­ing three let­ters.

The prac­tice of tak­ing an in­trade­pen­dent en­cod­ing and find­ing a more effi­cient one is known as com­pres­sion.