Coding apparatus, coding method, and coding system

A first prediction unit performs intra-prediction of an original image corresponding to an inter-frame coded frame to produce a first prediction residual and a prediction parameter. A second prediction unit performs intra-prediction of local decode data corresponding to the inter-frame coded data with the prediction parameter to produce a second prediction residual. A subtractor calculates difference data between the first prediction residual and the second prediction residual. A third prediction unit performs intra-prediction of data corresponding to a decoded frame with the prediction parameter to produce a third prediction residual, when the inter-frame coded data is decoded and transformed into the intra-frame coded data. An adder calculates addition data of the third prediction residual and the differential data. An intra-frame coding unit performs intra-frame coding to the addition data.