Systems and methods for enabling communication with a wired sensor are provided. The dither matrix includes a single reference matrix that is set by determining threshold values in the reference matrix based on a predetermined index value being calculated based on an arrangement pattern of at least two colors of dot groups among M colors of dot groups among the at least N colors of dot groups, with respect to at least some tone values among the input tone values. After the point p has been calculated, points a and b are detected by interrupting a predetermined time drive current. Parity processing units update parity information corresponding to row positions in p1 columns of each of the n1 column blocks of the first parity-check matrix, and corresponding to row positions in p2 columns of each of the n2 column blocks of the second parity-check matrix, a bit at each of the row positions being set to \u201c1\u201d.