Variable-Length Coding of Two-Sided Asymptotically Mean Stationary Measures

We collect several observations that concern variable-length coding of two-sided infinite sequences in a probabilistic setting. Attention is paid to images and preimages of asymptotically mean stationary measures defined on subsets of these sequences. We point out sufficient conditions under which the variable-length coding and its inverse preserve asymptotic mean stationarity. Moreover, conditions for preservation of shift-invariant $\sigma$-fields and the finite-energy property are discussed and the block entropies for stationary means of coded processes are related in some cases. Subsequently, we apply certain of these results to construct a stationary nonergodic process with a desired linguistic interpretation.Comment: 20 pages. A few typos corrected after the journal publicatio

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

Rivest,"Complete variable-length fix-free codes

Abstract. A set of codewords isfix-free if it is both prefix-free and suffix-free: no codeword in the set is a prefix or a suffix of any other. A set of codewords {Xl, x2..... x, } over a t-letter alphabet E is said to be complete if it satisfies the Kraft inequality with equality, so that ~t-lxl] =. 1 l<_i<n The set E k of all codewords of length k is obviously both fix-free and complete. We show, surprisingly, that there are other examples of complete fix-free codes, ones whose codewords have a variety of lengths. We discuss such variable-length (complete) fix-free codes and techniques for constructing them. 1