Preferred Design of Hierarchical Distribution Matching

Distribution matching and dematching (DM/invDM) are key functions in probabilistic shaping (PS). Recently techniques for low complexity implementation of DM/invDM have been well studied. Our previously proposed hierarchical DM (HiDM) is one of the good candidates, with capacity-approaching performance with reasonable hardware resources. Though we explained the recipe of HiDM construction with a small example having a short DM word length, there might still be difficulties to expand it to longer DM word lengths. To improve the reproducibility of our work, this paper explains the key parameters in an HiDM having a DM word length more than 100 symbols.