Binary prefix codes ending in a “1”

Binary prefix codes with the constraint that each codeword must end with a “1” have been recently introduced by Berger and Yeung (1990). We analyze the performance of such codes by investigating their average codeword length. In particular, we show that a very simple strategy permits the construction of a “1”-ended binary prefix code whose average codeword length is less than H+1 for any discrete source with entropy H. We also prove a tight lower bound on the optimal average codeword length in terms of H and of the minimum letter probability of the source. Finally, we discuss the problem of finding an optimum feasible code