ECC for component failures using Galois fields

A computer system comprising:

• at least one processor;
• at least one memory comprising a plurality of memory devices;
• and
• at least one memory controller coupled to the processor and to the memory, wherein the memory controller is coupled to receive data blocks from the processor for storage in the memory and coupled to provide data blocks read from the memory to the processor, and wherein the memory controller is configured to generate a corresponding encoded data block in response to receive a data block from the processor, the encoded data block including a first plurality of check bits, a second plurality of check bits, and the data block, and wherein the memory controller is configured to detect an error in data from one of the plurality of memory devices and correct the error using the first plurality of check bits, the second plurality of check bits, and the data block within the encoded data block;
• wherein the encoded data block is logically arranged as an array of R rows and N columns, wherein R and N are positive integers, and wherein each of the N columns comprises data bits from a respective one of the plurality of memory devices, and wherein the first plurality of check bits form a first column of the array, and wherein each of the first plurality of check bits covers a row of the array, and wherein the second plurality of check bits form a second column of the array and are defined to cover bits in the array according to a plurality of check vectors, each of the plurality of check vectors corresponding to a different bit in the array, and each of the plurality of check vectors is an element of a Galois Field (GF(2R)), and wherein the plurality of check vectors are derived from a plurality of unique elements of GF(2R), each of the plurality of unique elements corresponding to a different column of the array, and wherein the check vector in row X of the column is the product, in GF(2R) of the unique element for that column and alphaX, wherein alpha is a primitive element of GF(2R).

A method comprising:

• receiving an encoded data block comprising a data block, a first plurality of check bits, and a second plurality of check bits;
• detecting an error in data of the encoded data block that is from one of a plurality of components;
• and
• correcting the error using the first plurality of check bits, the second plurality of check bits, and the data block within the encoded data block;
• wherein the encoded data block is logically arranged as an array of R rows and N columns, wherein R and N are positive integers, and wherein each of the N columns comprises data bits from a respective one of the plurality of components, and wherein the first plurality of check bits form a first column of the array, and wherein each of the first plurality of check bits covers a row of the array, and wherein the second plurality of check bits form a second column of the array and are defined to cover bits in the array according to a plurality of check vectors, each of the plurality of check vectors corresponding to a different bit in the array, and each of the plurality of check vectors is an element of a Galois Field (GF(2R)), and wherein the plurality of check vectors are derived from a plurality of unique elements of GF(2R), each of the plurality of unique elements corresponding to a different column of the array, and wherein the check vector in row X of the column is the product, in GF(2R) of the unique element for that column and alphaX, wherein alpha is a primitive element of GF(2R).