Reversible data hiding (RDH) has been extensively studied in the field of information security. In our previous work [1], an explicit implementation approaching the rate-distortion bound of RDH has been proposed. However, there are two challenges left in our previous method. Firstly, this method suffers from computing precision problem due to the use of arithmetic coding, which may cause the further embedding impossible. Secondly, it had to transmit the probability distribution of the host signals during the embedding/extraction process, yielding quite additional overhead and application limitations. In this paper, we first propose an RDH scheme that employs our recent asymmetric numeral systems (ANS) variant as the underlying coding framework to avoid the computing precision problem. Then, we give a dynamic implementation that does not require transmitting the host distribution in advance. The simulation results show that the proposed static method provides slightly higher peak signal-to-noise ratio (PSNR) values than our previous work, and larger embedding capacity than some state-of-the-art methods on gray-scale images. In addition, the proposed dynamic method totally saves the explicit transmission of the host distribution and achieve data embedding at the cost of a small image quality loss.