This paper proposes a new lossless data compression coding scheme named an asymmetric encoding-decoding scheme (AEDS), which can be considered as a generalization of tANS (tabled variant of asymmetric numeral systems) although the class of the AEDS is much wider than the class of the tANS. In this paper, we explain the principle of the AEDS, and evaluate the average code length of the AEDS for several cases.