665 research outputs found
More Efficient Algorithms and Analyses for Unequal Letter Cost Prefix-Free Coding
There is a large literature devoted to the problem of finding an optimal
(min-cost) prefix-free code with an unequal letter-cost encoding alphabet of
size. While there is no known polynomial time algorithm for solving it
optimally there are many good heuristics that all provide additive errors to
optimal. The additive error in these algorithms usually depends linearly upon
the largest encoding letter size.
This paper was motivated by the problem of finding optimal codes when the
encoding alphabet is infinite. Because the largest letter cost is infinite, the
previous analyses could give infinite error bounds. We provide a new algorithm
that works with infinite encoding alphabets. When restricted to the finite
alphabet case, our algorithm often provides better error bounds than the best
previous ones known.Comment: 29 pages;9 figures
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
Huffman Coding with Letter Costs: A Linear-Time Approximation Scheme
We give a polynomial-time approximation scheme for the generalization of
Huffman Coding in which codeword letters have non-uniform costs (as in Morse
code, where the dash is twice as long as the dot). The algorithm computes a
(1+epsilon)-approximate solution in time O(n + f(epsilon) log^3 n), where n is
the input size
Infinite anti-uniform sources
6 pagesInternational audienceIn this paper we consider the class of anti-uniform Huffman (AUH) codes for sources with infinite alphabet. Poisson, negative binomial, geometric and exponential distributions lead to infinite anti-uniform sources for some ranges of their parameters. Huffman coding of these sources results in AUH codes. We prove that as a result of this encoding, we obtain sources with memory. For these sources we attach the graph and derive the transition matrix between states, the state probabilities and the entropy. If c0 and c1 denote the costs for storing or transmission of symbols "0" and "1", respectively, we compute the average cost for these AUH codes
- …