Low-complexity decoder and operation method thereof

A decoder comprising:

• a syndrome generator configured to generate a first syndrome, a second syndrome, and a third syndrome based on a reception vector and on a parity check matrix and to output the first syndrome, the second syndrome, and the third syndrome;
• and
• an error pattern classifier configured to:
• receive the first syndrome;
• obtain symbol error location information obtained based on mapping information between a spotty and adjacent symbol error (SASE) and the first syndrome;
• change the first syndrome to a normalized syndrome based on a first received symbol;
• obtain an adjacent error vector based on mapping information between the normalized syndrome, the second syndrome, and the third syndrome and the SASE;
• and
• correct an error of the reception vector based on the symbol error location information and the adjacent error vector,
• wherein the SASE is an error pattern based on adjacency between erroneous bits among bits in a 2-dimensional array, a number of error bits within the adjacency, and a length of the first received symbol.

An operation method of a decoder, the operation method comprising:

• generating a first syndrome, a second syndrome, and a third syndrome based on a reception vector and a parity check matrix;
• obtaining symbol error location information based on mapping information between a spotty and adjacent symbol error (SASE) and the first syndrome;
• changing the first syndrome to a normalized syndrome based on a first received symbol;
• obtaining an adjacent error vector based on mapping information between the normalized syndrome, the second syndrome, and the third syndrome and the SASE;
• and
• correcting an error of the reception vector based on the symbol error location information and the adjacent error vector,
• wherein the SASE is an error pattern based on adjacency between erroneous bits, a number of error bits within the adjacency, and a length of the first received symbol.