Full decodable code-word sets
M. P. Schützenberger, Richard S. Marcus · IEEE Transactions on Information Theory · 1959
This paper considers further how the decodability condition imposes restrictions on a set of code words. A generating function is defined that describes the composition of the code words. The relation between the generating function and a "full" set of code words is found. This relation shows that the sum of arbitrary probabilities associated with the words of a full set must be one. A full set of code words is one to which no code word can be added and still keep the set decodable. It is also shown that a full set is "completable." For a completable set of code words any string of symbols can be made into a sentence by adding a suitable prefix and a suffix.