239 research outputs found
On the Construction of Prefix-Free and Fix-Free Codes with Specified Codeword Compositions
We investigate the construction of prefix-free and fix-free codes with
specified codeword compositions. We present a polynomial time algorithm which
constructs a fix-free code with the same codeword compositions as a given code
for a special class of codes called distinct codes. We consider the
construction of optimal fix-free codes which minimizes the average codeword
cost for general letter costs with uniform distribution of the codewords and
present an approximation algorithm to find a near optimal fix-free code with a
given constant cost
On vocabulary size of grammar-based codes
We discuss inequalities holding between the vocabulary size, i.e., the number
of distinct nonterminal symbols in a grammar-based compression for a string,
and the excess length of the respective universal code, i.e., the code-based
analog of algorithmic mutual information. The aim is to strengthen inequalities
which were discussed in a weaker form in linguistics but shed some light on
redundancy of efficiently computable codes. The main contribution of the paper
is a construction of universal grammar-based codes for which the excess lengths
can be bounded easily.Comment: 5 pages, accepted to ISIT 2007 and correcte
Universal codes of the natural numbers
A code of the natural numbers is a uniquely-decodable binary code of the
natural numbers with non-decreasing codeword lengths, which satisfies Kraft's
inequality tightly. We define a natural partial order on the set of codes, and
show how to construct effectively a code better than a given sequence of codes,
in a certain precise sense. As an application, we prove that the existence of a
scale of codes (a well-ordered set of codes which contains a code better than
any given code) is independent of ZFC.Comment: 11 page
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