String Matching Bounds Via Coding

It is known that the length L(xn 1) 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(xn 1) 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.