Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 2 / 3I / b / Solution

For a source $(X_n)$ and fixed positive integer $N$, form the block source $Y_i=(X_{(i-1)N+1},\ldots,X_{iN})$. Whenever the original information rate $h$ exists, the blocked source has information rate $Nh$, because
$$
\frac1mH(Y_1,\ldots,Y_m)
=N\frac1{mN}H(X_1,\ldots,X_{mN}).
$$


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 Incoming links: Information rate under fixed-length blocking