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Path-invariant comma-free codes

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2 Author(s)

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 .

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Information Theory, IRE Transactions on  (Volume:8 ,  Issue: 6 )