On multiset decipherable codes (Corresp.)

Abstract

In certain applications it is necessary to communicate a description of a sequence of events where the information of interest is which one of a set of possible events has occurred, including multiplicity, but where the order of occurrence is irrelevant. Typical examples are online compilations of inventories, construction of histograms, or updating of relative frequencies. Suitable codes for this purpose need not be uniquely decipherable (UD). In fact, all that is required of such a code is that given a finite message over the code, every possible parsing of the message into codewords must yield the same multiset of codewords. A code with this property is referred to as a multiset decipherable (MSD) code. An MSD code is said to be proper if it is not a UD code. It is shown that for every n > 3 there exist proper MSD codes with n words. For n=2 , every MSD code is necessarily a UD code and all evidence points to the same conclusion for n=3 . It is further shown that no MSD code contains a full prefix code or a full suffix code as a proper subcode, and it is conjectured that despite the weaker decipherability condition, every MSD code satisfies the Kraft Inequality.