A decoder including a main memory, a flag memory and a decoding logic is provided. The flag memory is configured to store flag data and the decoding logic configured to perform an iteration. Further, the decoding logic is configured to: perform an ith operation using first data, wherein i is a natural number, flag-encode second data that is results obtained by performing the ith operation on the first data, store results obtained by performing the flag encoding on the second data in the flag memory as first flag data if the flag encoding succeeds, and store predetermined second flag data that is different from the first flag data of the second data in the flag memory if the flag encoding fails.