1. An encoding device comprising: a receiving unit that receives a shape of an image element convoluted with a binary halftone dot pattern; a shape encoding unit that separates the shape of the image element from the binary halftone dot pattern and encodes the shape of the image element received by the receiving unit; a pattern encoding unit that separates the binary halftone dot pattern from the shape of the image element and encodes the binary halftone dot pattern received by the receiving unit; an output unit that outputs the encoded binary halftone dot pattern and the encoded shape of the image element; and a processor that controls the receiving unit, the shape encoding unit, the pattern encoding unit and the output unit, wherein the shape encoded by the shape encoding unit and the binary halftone dot pattern encoded by the pattern encoding unit are encoded so as to-be paired with each other.