Quantized Indexing: Background Information

This report presents background material for the Quantized Indexing (QI) form of enumerative coding. Following the introduction to conventional enumerative coding and its reformulation as lattice walks, the relations between arithmetic and enumerative coding are explored. In addition to examining the fundamental origins of the performance differences (in speed and output size), special emphasis was on the distinctions in the two approaches to modeling. General modeling pattern for enumerative coding (including QI) is described, along with the special cases for finite order Markov sources. This approach is compared to the arithmetic coder adaptive modeling as well as to the grammer and dictionary based modeling methods. 1stWorks Corporation 30 Noon Hill Avenue Norfolk, MA 02056, USA Tel: (508) 541-6781 Email: [email protected] Web: http://www.1stWorks.com * 1stWorks Tech. Report TR05-0625, June 25, 2005, http://www.1stWorks.com/ref/tr/TR05-0625.pdf † Chief Scientist and CTO, 1stWorks Corp., [email protected] , Lexington MA 02421 ‡ Parts of this report are based on the 1stWorks TR04-0815 (henceforth [TR1]) from which it reuses the equation numbers. Due to the omitted materials from [TR1], there are some numbering gaps in the equations here. § For extended reference, online papers, tech. reports and code: http://www.1stWorks.com/ref/qi.htm