Path-invariant comma-free codes

In this paper we define a subclass of comma-free codes which has a property called path invariance. The main advantage of codes in this subclass lies in the ease of establishing the positions of the divisions between words. Certain path-invariant comma-free dictionaries using
K
symbols to form n-symbol words are developed and their properties are studied. The number of words in these dictionaries is determined to be
L(K-L)^{[n/2]}K^{[(n-1)/2]}
where
L
is a parameter which equals one when
n \geq 4K/3
, and
[x]
denotes the integral part of
x
. That this is the maximum obtainable dictionary size is proved for a special case. The ability of these codes to correct registration (synchronization) errors when
n
consecutive symbols are available (as opposed to the
2n
consecutive symbols required by general fixed-word-length comma-free codes) is demonstrated. A comparison of dictionary sizes is made for path-invariant comma-free codes, general fixed-word-length comma-free codes, and codes using one symbol as a comma. In the range
K \leq 6
and
n \leq 9
the path-invariant dictionaries are about
\frac{1}{2}
to
\frac{3}{4}
the size of the corresponding general comma-free dictionaries. Asymptotic dictionary sizes are obtained for
K \rightarrow \infty
and for
n \rightarrow \infty
.