Detection and correction of errors using limited error correction data

A system comprising:

• a memory system;
• and
• one or more processing units operatively coupled to the memory system, the one or more processing units to:
• obtain a codeword generated by a computer operation applied to an original codeword, wherein the original codeword encodes a plurality of symbols;
• compute, using the codeword, a plurality of syndrome values characterizing a difference between the codeword and the original codeword;
• identify a reduced set of error locator polynomials (ELPs) for the codeword, wherein each ELP of the reduced set of ELPs is associated with (i) at least one potential error within a respective group of symbols of a plurality of groups of symbols of the codeword and (ii) absence of potential errors outside the respective group of symbols;
• select, in view of the plurality of syndrome values, an indicator ELP from the reduced set of ELPs, wherein the indicator ELP is associated with a corrupted group of symbols of the plurality of groups of symbols, the corrupted group of symbols having at least one error;
• and
• identify, using the indicator ELP, the corrupted group of symbols.

A system comprising:

• a plurality of memory devices;
• a first set of one or more processing circuits to:
• receive, from the plurality of memory devices, a codeword comprising a plurality of symbols, wherein each of the plurality of symbols is received from a corresponding memory device of the plurality of memory devices, and wherein the codeword has at least one error relative to an original codeword stored in the plurality of memory devices;
• and
• compute, using the codeword, a plurality of syndrome values characterizing a difference between the codeword and the original codeword;
• a second set of one or more processing circuits to:
• identify a reduced set of error locator polynomials (ELPs) for the codeword, wherein each ELP of the reduced set of ELPs is associated with (i) at least one potential error within a respective group of symbols of a plurality of groups of symbols of the codeword and (ii) absence of potential errors outside the respective group of symbols;
• and
• select, in view of the plurality of syndrome values, an indicator ELP from the reduced set of ELPs, wherein the indicator ELP is associated with a corrupted group of symbols of the plurality of groups of symbols, the corrupted group of symbols having at least one error;
• and
• a third set of one or more processing circuits to:
• perform a plurality of iterations, wherein each iteration updates an iterative ELP based on a respective syndrome value of the plurality of syndrome values;
• update the iterative ELP, obtained after the plurality of iterations, using a difference between the iterative ELP and the indicator ELP, to obtain a final iterative ELP;
• and
• obtain the original codeword using the codeword and the final iterative ELP.