The Rényi redundancy of generalized Huffman codes

@article{Blumer1988TheRR,
  title={The R{\'e}nyi redundancy of generalized Huffman codes},
  author={Anselm Blumer and Robert J. McEliece},
  journal={IEEE Trans. Inf. Theory},
  year={1988},
  volume={34},
  pages={1242-1249}
}
Huffman's algorithm gives optimal codes, as measured by average codeword length, and the redundancy can be measured as the difference between the average codeword length and Shannon's entropy. If the objective function is replaced by an exponentially weighted average, then a simple modification of Huffman's algorithm gives optimal codes. The redundancy can now be measured as the difference between this new average and A. Renyi's (1961) generalization of Shannon's entropy. By decreasing some of… 
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References

SHOWING 1-10 OF 11 REFERENCES
Variations on a theme by Huffman
TLDR
Four new results about Huffman codes are presented and a simple algorithm for adapting a Huffman code to slowly varying esthnates of the source probabilities is presented.
A Coding Theorem and Rényi's Entropy
Buffer overflow in variable length coding of fixed rate sources
  • F. Jelinek
  • Computer Science
    IEEE Trans. Inf. Theory
  • 1968
In this paper, we develop and analyze an easily instrumentable scheme for variable length encoding of discrete memoryless fixed-rate sources in which buffer overflows result in codeword erasures at
Generalization of Huffman coding to minimize the probability of buffer overflow
  • P. Humblet
  • Computer Science
    IEEE Trans. Inf. Theory
  • 1981
An algorithm is given to find a prefix condition code that minimizes the value of the moment generating function of the codeword length distribution for a given positive argument. This algorithm is
Conditions for Optimality of the Huffman Algorithm
TLDR
A new general formulation of Huffman tree construction is presented which has broad application and a wide class of weight combination functions, the quasilinear functions, for which the Huffman algorithm produces optimal trees under correspondingly wide classes of cost criteria are characterized.
An Introduction to the Theory of Numbers
  • E. T.
  • Mathematics
    Nature
  • 1946
THIS book must be welcomed most warmly into X the select class of Oxford books on pure mathematics which have reached a second edition. It obviously appeals to a large class of mathematical readers.
BINARY TREES OPTIMUM UNDER VARIOUS CRITERIA
TLDR
It is shown that Hu–Tucker type algorithms can be used to find trees, whose leaves preserve a given order, that minimizing certain sums of functions of path length, and also that minimize certain maximum functions of paths length.
Kricevski, "The block length necessary to obtain a given redundancy," Sou
  • Math. Dokl.,
  • 1966
The block length necessary to obtain a given redundancy
  • Sou. Math. Dokl
  • 1966
...
...