In the Dictionary-based String Matching (DSM) problem, an Information Retrieval (IR) system has access to a source sequence and stores the position of a certain number of strings in a posting table. When a user inquires the position of a string, the IR system, instead of searching in the source sequence directly, relies on the the posting table to answer the query more efficiently. In this paper, the Statistical DSM problem is proposed as a statistical and information-theoretic formulation of the classic DSM problem in which both the source and the query have a statistical description while the strings stored in the posting sequence are described as a code. Through this formulation, we define the communication efficiency of the IR system as the average cost in retrieving the entries of the posting list from the posting table, in the limit of an infinitely long source sequence. This formulation is used to study the communication efficiency for the case in which the dictionary is composed of (i) all the strings of a given length, referred to as k-grams, and (ii) run-length codes.