The <asymptotic equipartition property> is $-n^{-1}\log_2p(X_1,\ldots,X_n)\to H$ in probability. For an i.i.d. source this is the weak law applied to $-\log_2p(X_i)$, and independence gives $H(X_1,\ldots,X_n)=nH(X)$. Thus its <information rate> and AEP constant are both $H(X)$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 2 / 3H / d / Solution

 Solution (source code)