  In this paper, we consider the so-called uniquely decodable one-to-one code
(UDOOC) that is formed by inserting a "comma" indicator, termed the unique word
(UW), between consecutive one-to-one codewords for separation. Along this
research direction, we first investigate several general combinatorial
properties of UDOOCs, in particular the enumeration of the number of UDOOC
codewords for any (finite) codeword length. Based on the obtained formula on
the number of length-n codewords for a given UW, the per-letter average
codeword length of UDOOC for the optimal compression of a given source
statistics can be computed. Several upper bounds on the average codeword length
of such UDOOCs are next established. The analysis on the bounds of average
codeword length then leads to two asymptotic bounds for sources having
infinitely many alphabets, one of which is achievable and hence tight for a
certain source statistics and UW, and the other of which proves the
achievability of source entropy rate of UDOOCs when both the block size of
source letters for UDOOC compression and UW length go to infinity. Efficient
encoding and decoding algorithms for UDOOCs are also given in this paper.
Numerical results show that the proposed UDOOCs can potentially result in
comparable compression rate to the Huffman code under similar decoding
complexity and yield a smaller average codeword length than that of the
Lempel-Ziv code, thereby confirming the practicability of UDOOCs.
