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Under what conditions does Huffman encoding make a string not compressible? Is it when all the characters appear with equal frequency/probability? And if so, how can one show this is true?
In a nutshell, Huffman encoding assigns smaller bit-length codes to more probable binary combinations and longer ones to the less probable ones. If all are equally likely, you will find there is no real advantage because the compression due to shorter codes is lost due to equally likely longer codes.