INFINITE ANTI - UNIFORM SOURCES WITH GEOMETRIC DISTRIBUTION

11 pagesInternational audienceIn this paper we consider the class of anti-uniform Huffman (AUH) codes for sources with infinite alphabet generated by geometric distribution. Huffman encoding of these sources results in AUH codes. As a result of this encoding, we obtain sources with memory. The entropy and average cost of these sources with memory are derived. We perform an analogy between sources with memory and discrete memoryless channels, showing that the entropy of the source with memory is similar to the mean error of the discrete memoryless channel. The information quantity I(X,S) specifies for AUH codes whether they are with memory or not, as it differs from zero or is equal to zero, respectively

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

Lower Bounds on the Redundancy of Huffman Codes with Known and Unknown Probabilities

In this paper we provide a method to obtain tight lower bounds on the minimum redundancy achievable by a Huffman code when the probability distribution underlying an alphabet is only partially known. In particular, we address the case where the occurrence probabilities are unknown for some of the symbols in an alphabet. Bounds can be obtained for alphabets of a given size, for alphabets of up to a given size, and for alphabets of arbitrary size. The method operates on a Computer Algebra System, yielding closed-form numbers for all results. Finally, we show the potential of the proposed method to shed some light on the structure of the minimum redundancy achievable by the Huffman code

Some basic properties of fix-free codes.

by Chunxuan Ye.Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.Includes bibliographical references (leaves 74-[78]).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Information Theory --- p.1Chapter 1.2 --- Source Coding --- p.2Chapter 1.3 --- Fixed Length Codes and Variable Length Codes --- p.4Chapter 1.4 --- Prefix Codes --- p.5Chapter 1.4.1 --- Kraft Inequality --- p.7Chapter 1.4.2 --- Huffman Coding --- p.9Chapter 2 --- Existence of Fix-Free Codes --- p.13Chapter 2.1 --- Introduction --- p.13Chapter 2.2 --- Previous Results --- p.14Chapter 2.2.1 --- Complete Fix-Free Codes --- p.14Chapter 2.2.2 --- Ahlswede's Results --- p.16Chapter 2.3 --- Two Properties of Fix-Free Codes --- p.17Chapter 2.4 --- A Sufficient Condition --- p.20Chapter 2.5 --- Other Sufficient Conditions --- p.33Chapter 2.6 --- A Necessary Condition --- p.37Chapter 2.7 --- A Necessary and Sufficient Condition --- p.42Chapter 3 --- Redundancy of Optimal Fix-Free Codes --- p.44Chapter 3.1 --- Introduction --- p.44Chapter 3.2 --- An Upper Bound in Terms of q --- p.46Chapter 3.3 --- An Upper Bound in Terms of p1 --- p.48Chapter 3.4 --- An Upper Bound in Terms of pn --- p.51Chapter 4 --- Two Applications of the Probabilistic Method --- p.54Chapter 4.1 --- An Alternative Proof for the Kraft Inequality --- p.54Chapter 4.2 --- A Characteristic Inequality for ´ب1´ة-ended Codes --- p.59Chapter 5 --- Summary and Future Work --- p.69Appendix --- p.71A Length Assignment for Upper Bounding the Redundancy of Fix-Free Codes --- p.71Bibliography --- p.7