Fast polynomial division by monomial for Reed-Solomon ELP maintenance

A device for decoding a codeword which comprises a plurality of frames, the device comprising:

• at least one processor configured to:
• obtain an initial error locator polynomial (ELP) corresponding to the codeword;
• decode a frame of the plurality of frames;
• based on the frame being successfully decoded, determine an updated ELP by simultaneously calculating at least two updated coefficients from among a plurality of updated coefficients included in the updated ELP;
• and
• obtain information bits corresponding to the codeword based on the updated ELP.

A method of controlling a storage system, the method being executed by at least one processor and comprising:

• obtaining a codeword from a storage device, wherein the codeword comprises a plurality of frames;
• obtaining an initial error locator polynomial (ELP) corresponding to the codeword;
• decoding a frame of the plurality of frames;
• based on the frame being successfully decoded, determining an updated ELP based on the initial ELP and information about the frame;
• and
• obtaining information bits corresponding to the codeword based on the updated ELP,
• wherein the updated ELP comprises a plurality of updated coefficients, and
• wherein the determining the updated ELP comprises simultaneously calculating at least two updated coefficients from among the plurality of updated coefficients.