Redundancy and Optimization of tANS Entropy Encoders

Abstract

Nowadays entropy encoders are part of almost all data compression methods, with the Asymmetrical Numeral Systems (ANS) family of entropy encoders having recently risen in popularity. Entropy encoders based on the tabled variant of ANS are known to provide varying performances depending on their internal design. In this paper, we present a method that calculates encoder redundancies in almost linear time, which translates in practice to thousand-fold speedups in redundancy calculations for small automatons, and allows redundancy calculations for automatons with tens of millions of states that would be otherwise prohibitive. We also address the problem of improving tabled ANS encoder designs, by employing the aforementioned redundancy calculation method in conjunction with a stochastic hill climbing strategy. The proposed approach consistently outperforms state-of-the-art methods in tabled ANS encoder design. For automatons of twice the alphabet size, experimental results show redundancy reductions around 10% over the default initialization method and over 30% for random initialization.

Fast and Efficient Entropy Coding Architectures for Massive Data Compression

“…To this end, the top table depicted in Figure 4 is transformed into a finite-state machine, with the coding of each symbol being state transitions. There exist many different automatons for each distribution [46], so a key K that represents a unique scheme needs to be chosen first. A suitable key for the distribution of the above example might be K = 001001 since it strictly respects p(x = 0) = 2/3.…”

“…As with V2VLC, the selection of the key that achieves the lowest redundancy uses a full search approach since this process is carried out before coding. Some strategies to accelerate the selection of K can be found in [46].…”

“…The decoder reverses the path from the last to the first group, recovering the original symbols. There are different variants of ANS such as the range ANS or the uniform binary ANS, though the tabled ANS (tANS) is the most popular [45][46][47] since it can operate like a finite-state machine achieving high throughput. tANS has been recently adopted in many compression schemes [11,48,49], so it is employed in this work to represent this family of entropy coders.…”

The Efficiency of the ANS Entropy Encoding

“…Since the invention of ANS and the emergence of its efficient implementation by Collet [7], several high performance compressors based on ANS appeared [1,6,16] and it was integrated in some modern media formats [2,3]. The theoretical community also contributed to the study of ANS in a series of works [4,13,20,23,24,25], though less actively than the practitioners [5,8,15,16].…”