A decoding apparatus includes a dequantization-value generating section, distribution-information acquiring section, and a correcting section. The dequantization-value generating section generates a plurality of dequantization values for each quantization index value. The distribution-information acquiring section acquires distribution information of original data corresponding to each quantization index. The correcting section corrects at least a portion of the dequantization values generated by the dequantization-value generating section, based on the distribution information acquired by the distribution-information acquiring section.