# 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…

## 43 Citations

Redundancy-Related Bounds for Generalized Huffman Codes

- Computer ScienceIEEE Transactions on Information Theory
- 2011

New lower and upper bounds for the compression rate of binary prefix codes optimized over memoryless sources according to various nonlinear codeword length objectives are presented, which relate to various problems involving queueing, uncertainty, and lossless communications.

Bounds on Generalized Huffman Codes

- Computer ScienceArXiv
- 2007

New lower and upper bounds are obtained for the compression of optimal binary prefix codes according to various nonlinear codeword length objectives in terms of a form of entropy and the probability of the most probable input symbol.

Source Coding for Quasiarithmetic Penalties

- Computer ScienceIEEE Transactions on Information Theory
- 2006

Several cost functions are shown here to yield quasiarithmetic problems with simple redundancy bounds in terms of a generalized entropy, which reduces the computational complexity of a problem involving minimum delay in a queue, allows combinations of previously considered problems to be optimized, and greatly expands the set of problems solvable in quadratic time and linear space.

On the redundancy of Huffman codes with exponential objectives

- Computer Science2013 IEEE International Symposium on Information Theory
- 2013

New lower and upper bounds for the compression rate of binary prefix codes over memoryless sources optimized according to two related exponential codeword length objectives are presented, improving on recently discovered bounds of similar form.

Redundancy-Related Bounds for

- Computer Science
- 2011

New lower and upper bounds for the compression rate of binary prefix codes optimized over memo- ryless sources according to various nonlinear codeword length ob- jectives are presented, which relates to various problems involving queueing, un- certainty, and lossless communications.

New Upper and Lower Bounds on Exponentially Weighted Average Length of Optimal Binary Prefix Codes

- Computer Science2006 IEEE Information Theory Workshop - ITW '06 Chengdu
- 2006

Under Campbell's average codeword length criterion, new upper and lower bounds on the exponentiated expected length of optimal binary prefix codes when partial information about the source symbol probabilities is available are derived.

Upper bounds on exponentiated expected length of optimal one-to-one codes

- Computer ScienceIWCMC '06
- 2006

An exponentially weighted average codeword length introduced by Campbell as a performance measure for source codes is considered and several new upper bounds on Campbell's average length of optimal one-to-one codes when the probability of the most likely source symbol is available are obtained.

Prefix Coding under Siege

- Computer ScienceArXiv
- 2006

A novel lossless source coding paradigm applies to problems in which a vital message needs to be transmitted prior to termination of communications, as in Alfr éd Rényi’s secondhand account of an…

Optimal Prefix Codes for Infinite Alphabets With Nonlinear Costs

- Computer ScienceIEEE Transactions on Information Theory
- 2008

Methods for finding codes optimal for beta-exponential means are introduced and one method applies to geometric distributions, while another applies to distributions with lighter tails and both are extended to alphabetic codes.

Infinite-Alphabet Prefix Codes Optimal for beta-Exponential Penalties

- Computer ScienceArXiv
- 2007

Methods for finding codes optimal for exponential means of Poisson distributions are introduced, one of which applies to geometric distributions, while another applies to distributions with lighter tails.

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