An error correction apparatus includes an error correction circuit configured to selectively perform error correction on a portion of data that is at least one of written to and read from a plurality of memory cells of a memory device. The portion of data is at least one of written to and read from a subset of the plurality of memory cells, and the subset includes only fail cells among the plurality of memory cells. The error correction apparatus further includes a fail address storage circuit configured to store address information for the fail cells.