Construction of minimum-redundance codes with an optimum synchronizing property

A simple method has been found for constructing a minimum-redundancy code having the shortest possible synchronizing sequence. For most variable-length codes the propagation of an error is halted by the next appearance of certain naturally occurring synchronizing sequences. Although the time between error and resynchronization has no upper bound, the length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</tex> of the shortest resynchronizing sequence is a useful measure of its expected value. Since a finite set of messages with specified probabilities can usually be matched with maximum efficiency by many codes having widely different values of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</tex> , a nonexhaustive method for finding a code with minimum <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</tex> is of interest. The method presented is valid for a class of message sets that includes, among those discussed in the literature, the set of English letters, and two listings of roughly 5000 English words.