It is known that the length $L(x_1^n)$ of the longest block
appearing at least twice in a randomly chosen sample path of length $n$ drawn
from an i.i.d. process is asymptotically almost surely equal to $C \log n$,
where the constant $C$ depends on the process. A simple coding argument will be
used to show that for a class of processes called the finite energy processes,
$L(x_1^n)$ is almost surely upper bounded by $C \log n$, where $C$ is a
constant. While the coding technique does not yield the exact constant $C$, it
does show clearly what is needed to obtain log $n$ bounds.