مرکز منطقه ای اطلاع رساني علوم و فناوري

Abstract :

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 $n \\rightarrow \\infty$ .