Journal of Algorithms
Design and analysis of dynamic Huffman codes
Journal of the ACM (JACM)
A fast algorithm for optimal length-limited Huffman codes
Journal of the ACM (JACM)
Coding and Information Theory
Exact and Experimental Algorithms for a Huffman-Based Error Detecting Code
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Variations on a theme by Huffman
IEEE Transactions on Information Theory
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Even codes are prefix-free codes where every encoding contains an even number of 1's, thus having ability of detecting the occurrence of an odd number of 1-bit errors in a message. The motivation for defining such codes comes from a problem posed by Hamming in 1980. Even codes have been studied for the case in which symbols have uniform probabilities. In this work, we consider the general case of arbitrary probabilities. An exact algorithm for constructing an optimal even code is described with complexity O(n^3), where n is the number of symbols. Further, two approximation algorithms for constructing nearly optimal even codes are presented, both requiring O(nlogn) time; in addition, the running time is O(n) if the symbols are given ordered by their probabilities. The cost of the even code constructed by the second approximation algorithm is at most 16.7% higher than the cost of a Huffman code, for the same probabilities. However, computational experiments suggest that, in practice, this difference is about 5%, for n large enough.