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.