# Source Coding for Quasiarithmetic Penalties

@article{Baer2006SourceCF, title={Source Coding for Quasiarithmetic Penalties}, author={Michael B. Baer}, journal={IEEE Transactions on Information Theory}, year={2006}, volume={52}, pages={4380-4393} }

Whereas Huffman coding finds a prefix code minimizing mean codeword length for a given finite-item probability distribution, quasiarithmetic or quasilinear coding problems have the goal of minimizing a generalized mean of the form rho-1(Sigmaipirho(li )), where li denotes the length of the ith codeword, p i denotes the corresponding probability, and rho is a monotonically increasing cost function. Such problems, proposed by Campbell, have a number of diverse applications. Several cost functions…

## 29 Citations

### 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 ß-Exponential Penalties

- Computer Science2007 IEEE International Symposium on Information Theory
- 2007

Methods for finding codes optimal for beta-exponential means are introduced, one of which applies to geometric distributions, while another applies to distributions with lighter tails, and both are extended to minimizing maximum pointwise redundancy.

### D-ary Length-Bounded Prefix Coding

- Computer Science
- 2008

Two algorithms used for length-limited prefix coding are generalized, without increasing complexity, in order to introduce a minimum codeword length constraint lmin and to be applicable to both binary and nonbinary 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.

### IT ] 1 N ov 2 00 5 Integer Coding with Nonlinear Costs

- Computer Science
- 2008

Algorithms for finding integer codes o ptimal for β-exponential means, which applies to geometric distributions, while another applies to distr ibutions with lighter tails, and both are extended to alphabeti c codes.

### Generalizations of Length Limited Huffman Coding for Hierarchical Memory Settings

- Computer Science
- 2020

This paper studies the problem of designing prefix-free encoding schemes having minimum average code length that can be decoded efficiently under a decode cost model that captures memory hierarchy induced cost functions and presents an algorithm to solve this problem in time O(nD).

### Twenty (or so) Questions: $D$-ary Length-Bounded Prefix Coding

- Computer ScienceArXiv
- 2006

These algorithms are generalized without increasing complexity in order to introduce a minimum codeword length constraint, to allow for objective functions other than the minimization of expected codewords length, and to be applicable to both binary and nonbinary codes; non binary codes were previously addressed using a slower dynamic programming approach.

### Lossless quantum data compression with exponential penalization: an operational interpretation of the quantum Rényi entropy

- Computer ScienceScientific Reports
- 2017

It is shown that by invoking an exponential average length, related to an exponential penalization over large codewords, the quantum Rényi entropies arise as the natural quantities relating the optimal encoding schemes with the source description, playing an analogous role to that of von Neumann entropy.

## References

SHOWING 1-10 OF 60 REFERENCES

### The Rényi redundancy of generalized Huffman codes

- Computer ScienceIEEE Trans. Inf. Theory
- 1988

By decreasing some of the codeword lengths in a Shannon code, the upper bound on the redundancy given in the standard proof of the noiseless source coding theorem is improved and the lower bound is improved by randomizing between codewords, allowing linear programming techniques to be used on an integer programming problem.

### Minimum Delay Codes

- Computer ScienceSIAM J. Comput.
- 1989

Huffman's algorithm finds a prefix-free binary code on a weighted alphabet which minimizes the expected length of the code string for a single symbol, and it is conjectured that the algorithm has substantially lower time and space complexities in the worst case, and still lower in the average case.

### Practical Length-limited Coding for Large Alphabets

- Computer ScienceComput. J.
- 1995

This work re-examine the package-merge algorithm for generating minimum-cost length-limited prefix-free codes and shows that with a considered reorganization of the key steps it is possible for it to run quickly in significantly less memory than was required by previous implementations, while retaining asymptotic efficiency.

### A Fast and Space - Economical Algorithm for Length - Limited Coding

- Computer ScienceISAAC
- 1995

The size of the work space can be reduced to O(L2), which represents a useful improvement, since for practical purposes L is Θ(log n).

### Existence of optimal prefix codes for infinite source alphabets

- Computer ScienceIEEE Trans. Inf. Theory
- 1997

It is proven that for every random variable with a countably infinite set of outcomes and finite entropy there exists an optimal prefix code which can be constructed from Huffman codes for truncated…

### Huffman codes and self-information

- Computer ScienceIEEE Trans. Inf. Theory
- 1976

In this paper the connection between the self-information of a source letter from a finite alphabet and its code-word length in a Huffman code is investigated. Consider the set of all independent…

### On the redundancy of optimal codes with limited word length

- Computer ScienceIEEE Trans. Inf. Theory
- 1992

It is shown that the redundancy of these constrained codes is very close to that of the unconstrained Huffman codes when the number of codewords N is such that ND/sup 1-L/ becomes negligible.

### Renyi to Renyi - Source Coding under Siege

- Computer Science2006 IEEE International Symposium on Information Theory
- 2006

A novel lossless source coding paradigm applies to problems of unreliable lossless channels with low bit rates, in which a vital message needs to be transmitted prior to termination of…

### A Fast Algorithm for Optimum Height-Limited Alphabetic Binary Trees

- Computer ScienceSIAM J. Comput.
- 1994

This algorithm is an alphabetic version of the Package Merge algorithm, and yields an O(nL\log n)-time algorithm for theAlphabetic Huffman coding problem, and appears hard to prove correct.