Trying to learn more about compression techniques and found something in the wikipedia article on arithmetic coding that I'm not sure I fully grok. In describing how Huffman Coding can sometimes be inefficient, the author refers to an 'optimal compression ratio' that seems to be a function of the probabilities of a given symbol being represented at any given position in the dataset. Am I correct in understanding this to mean:
Given a set of data and a set of probabilities describing the likelihood of any given member of the dataset being a given symbol, then there is no way to represent that data encoded in that manner in fewer bits than the calculated optimal compression ratio?
In other words: there's no way to encode something in few than 'optimal' bits so don't try?