Adaptive Numeral System (ANS) and its applications in data compression

Abstract

This research explores innovative methodologies for advancing lossless data compression by developing adaptive numeral systems to calculate and reduce binary data representations effectively. Building on the foundational theories of Shannon and Kolmogorov, the study introduces the Adaptive Numeral System (ANS), Improved Adaptive Numeral System (IANS), and Modified Adaptive Numeral System (MANS), novel approaches for adaptively calculating binary values. These systems can be shown to exhibit the unique capability of compressing each segment iteratively, thereby reducing the overall data size progressively and form the basis for an iterative and progressive approach to data compression. To leverage these adaptive numeral systems, the study presents the Data Extraction (DE) technique, a compression framework that uses MANS to perform conversions from binary values into more compact representations. DE achieves significant compression rates, demonstrating competitive performance compared to traditional methods like Huffman coding, particularly in its fully decodable state before binary conversion. Furthermore, the research addresses challenges in identifying flag locations within segmented data, proposing a range of solutions to enhance compression efficiency and reliability. The combined contributions of ANS, IANS, MANS, and DE represent a significant advancement in the field of lossless compression, particularly in their ability to process already compressed data and transform non-prefix codes into prefix codes. These advancements hold substantial promise for applications in areas such as medical imaging, digital media, machine learning, artificial intelligence, embedded systems, and the Internet of Things.