A Review of the Asymmetric Numeral System and Its Applications to Digital Images

The Asymmetric Numeral System (ANS) is a new entropy compression method that the industry has highly valued in recent years. ANS is valued by the industry precisely because it captures the benefits of both Huffman Coding and Arithmetic Coding. Surprisingly, compared with Huffman and Arithmetic coding, systematic descriptions of ANS are relatively rare. In 2017, JPEG proposed a new image compression standard—JPEG XL, which uses ANS as its entropy compression method. This fact implies that the ANS technique is mature and will play a kernel role in compressing digital images. However, because the realization of ANS involves combination optimization and the process is not unique, only a few members in the compression academia community and the domestic industry have noticed the progress of this powerful entropy compression approach. Therefore, we think a thorough overview of ANS is beneficial, and this idea brings our contributions to the first part of this work. In addition to providing compact representations, ANS has the following prominent feature: just like its Arithmetic Coding counterpart, ANS has Chaos characteristics. The chaotic behavior of ANS is reflected in two aspects. The first one is that the corresponding compressed output will change a lot if there is a tiny change in the original input; moreover, the reverse is also applied. The second is that ANS compressing an image will produce two intertwined outcomes: a positive integer (aka. state) and a bitstream segment. Correct ANS decompression is possible only when both can be precisely obtained. Combining these two characteristics helps process digital images, e.g., art collection images and medical images, to achieve compression and encryption simultaneously. In the second part of this work, we explore the characteristics of ANS in depth and develop its applications specific to joint compression and encryption of digital images.