Perplexity
A measure related to the notion of cross-entropy and used in the speech recognition community is called the perplexity.
Perplexity(x1n, m) =2H(x1n,m) =m(x1n)-1/n
A perplexity of k means that you are as surprised on average as you would have been if you had had to guess between k equiprobable choices at each step.