A lower bound on the redundancy of arithmetic-type delay constrained coding

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Abstract

In a previous paper we derived an upper bound on the redundancy of an arithmetic-type encoder for a memoryless source, designed to meet a finite end-to-end strict delay constraint. It was shown that the redundancy decays exponentially with the delay constraint and that the redundancy-delay exponent is lower bounded by log(l/α) where α is the probability of the most likely source symbol. In this work, we prove a corresponding upper bound for the redundancy-delay exponent, C · log 1/β where β is the probability of the least likely source symbol. This bound is valid for almost all memoryless sources and for all arithmetic-type (possibly time-varying, memory dependent) lossless delay-constrained encoders. We also shed some light on the difference between our exponential bounds and the polynomial O(d -5/3) upper bound on the redundancy with an average delay constraint d, derived in an elegant paper by Bugeaud, Drmota and Szpankowski for another class of variable-to-variable encoders, and show that the difference is due to the precision needed to memorize the encoder's state.

Original languageEnglish
Title of host publicationProceedings - 2008 Data Compression Conference, DCC 2008
Pages489-498
Number of pages10
DOIs
StatePublished - 2008
Event2008 Data Compression Conference, DCC 2008 - Snowbird, UT, United States
Duration: 25 Mar 200827 Mar 2008

Publication series

NameData Compression Conference Proceedings
ISSN (Print)1068-0314

Conference

Conference2008 Data Compression Conference, DCC 2008
Country/TerritoryUnited States
CitySnowbird, UT
Period25/03/0827/03/08

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