Low gate-count generalized concatenated code (GCC) by online calculation of syndromes instead of buffer

A device for decoding a generalized concatenated code (GCC) codeword, the device comprising:

• a buffer;
• and
• at least one processor configured to:
• obtain the GCC codeword, wherein the GCC codeword comprises a plurality of frames encoded according to an inner coding scheme and arranged as a plurality of rows, and each column of a plurality of columns corresponding to the plurality of rows is encoded according to an outer coding scheme;
• calculate a plurality of inner syndromes based on the plurality of frames, wherein the plurality of inner syndromes correspond to the inner coding scheme;
• calculate a plurality of sets of delta syndromes based on the plurality of frames;
• determine a plurality of outer syndromes based on the plurality of sets of delta syndromes, wherein the plurality of outer syndromes correspond to the outer coding scheme;
• store the plurality of inner syndromes and the plurality of outer syndromes in a buffer;
• perform inner decoding on the plurality of frames according to the inner coding scheme based on the plurality of inner syndromes stored in the buffer;
• update at least one outer syndrome of the plurality of outer syndromes stored in the buffer based on a result of the inner decoding;
• and
• perform outer decoding on the plurality of frames according to the outer coding scheme based on the updated at least one outer syndrome;
• and
• obtain decoded information bits corresponding to the GCC codeword based on a result of the inner decoding and the result of the outer decoding.

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

• obtaining, by an input processing module implemented by the at least one processor, a generalized concatenated code (GCC) codeword from a storage device, wherein the GCC codeword comprises a plurality of frames arranged according to a Super Bose-Chaudhuri-Hocquenghem (SBCH) coding scheme;
• calculating, by the input processing module, a plurality of Bose-Chaudhuri-Hocquenghem (BCH) syndromes based on the plurality of frames;
• calculating, by the input processing module, a plurality of sets of delta syndromes based on the plurality of frames;
• determining, by the input processing module, a plurality of Reed-Solomon (RS) syndromes based on the plurality of sets of delta syndromes;
• and
• storing, by the input processing module, the plurality of BCH syndromes and the plurality of RS syndromes in a buffer;
• obtaining, by a decoder module implemented by the at least one processor, the plurality of BCH syndromes and the plurality of RS syndromes from the buffer;
• performing, by the decoder module, BCH decoding on the plurality of frames based on the plurality of BCH syndromes;
• performing, by the decoder module, RS decoding on the plurality of frames based on the plurality of RS syndromes and a result of the BCH decoding;
• and
• obtaining, by an output processing module implemented by the at least one processor, decoded information bits corresponding to the GCC codeword based on a result of the RS decoding and the result of the BCH decoding.