Investigations on Algorithm Selection for Interval-Based Coding Methods

TL;DR

This paper compares different algorithmic approaches for interval-based entropy coding, focusing on symbol search and interval update efficiencies, and proposes a more flexible binary indexing variant to optimize adaptive compression performance.

Contribution

It introduces a detailed analysis of search and update methods for interval-based coding, and proposes a new flexible binary indexing variant to improve adaptive compression efficiency.

Findings

Binary indexing method outperforms others in adaptive mode.

Reducing complexity does not always speed up practical implementations.

Proposed variant offers greater flexibility and lower complexity.

Abstract

There is a class of entropy-coding methods which do not substitute symbols by code words (such as Huffman coding), but operate on intervals or ranges. This class includes three prominent members: conventional arithmetic coding, range coding, and coding based on asymmetric numeral systems. To determine the correct symbol in the decoder, each of these methods requires the comparison of a state variable with subinterval boundaries. In adaptive operation, considering varying symbol statistics, an array of interval boundaries must additionally be kept up to date. The larger the symbol alphabet, the more time-consuming both the search for the correct subinterval and the updating of interval borders become. Detailed pseudo-code is used to discuss different approaches to speed up the symbol search in the decoder and the adaptation of the array of interval borders, both depending on the chosen alphabet size. It is shown that reducing the $\mathcal{O}$-complexity does not lead to an acceleration in practical implementations if the alphabet size is too small. In adaptive compression mode, the binary indexing method proves to be superior when considering the overall processing time. Although the symbol search (in the decoder) takes longer than with other algorithms, the faster updating of the array of interval borders more than compensates for this disadvantage. A variant of the binary indexing method is proposed, which is more flexible and has a partially lower complexity than the original approach.