Shannon entropy


"That you can zip a large movie file, for example, owes to the fact that pixel colors have a statistical pattern, the way English words do. Engineers can build probabilistic models for patterns of pixel colors from one frame to the next. 

"The models make it possible to calculate the Shannon entropy by assigning weights to patterns and then taking the logarithm of the weight for all the possible ways pixels could appear. That value tells you the limit of lossless compression —the absolute most the movie can be compressed before you start to lose information about its contents.

"Any compression algorithm’s performance can be compared to this limit. If you’re far from it, you have an incentive to work harder to find a better algorithm. But if you’re close to it, you know that the information laws of the universe prevent you from doing much better."

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