Let us use 0 and 1 for the binary parallel.

You have 256 characters you need to reference, imagining a 256 character alphabet. You can only use a string to reference them that contains 0 and 1. The string can be any length, and your reference can have multiple levels of compression (as long as they would work for any combination of those 256 characters).

Is it possible to efficiently reference this 256 character alphabet this way?