Two-dimensional generalized concatenated codes with sub-fields

A method of controlling a storage system, the method comprising:

• obtaining a codeword from among a plurality of codewords stored in a storage device included in the storage system, wherein the codeword comprises a plurality of rows and a plurality of columns;
• generating a first transformed codeword by transforming each row of the plurality of rows, wherein the first transformed codeword comprises a plurality of first transformed rows and a plurality of first transformed columns;
• generating a second transformed codeword by transforming each column of the plurality of columns, wherein the second transformed codeword comprises a plurality of second transformed rows and a plurality of second transformed columns;
• and
• decoding the codeword to obtain information bits corresponding to the codeword, by performing iterative decoding on the first transformed codeword and the second transformed codeword,
• wherein after the codeword is decoded, a first plurality of syndromes calculated based on the plurality of first transformed columns is equal to a second plurality of syndromes calculated based on the plurality of second transformed rows.

A device for managing data stored in a storage device, the device comprising:

• a memory interface configured to communicate with the storage device;
• and
• at least one processor configured to:
• obtain a two-dimensional (2D) generalized concatenated code (GCC) codeword from the storage device,
• apply a sequential decoding process to the codeword,
• based on detecting a first failure, update the codeword and transpose the updated codeword to obtain a transposed codeword,
• apply the sequential decoding process to the transposed codeword to obtain a decoding result, and
• obtain information bits corresponding to the codeword based on the decoding result.