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ECC for component failures using Galois fields
ECC for component failures using Galois fields
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机译:使用Galois字段的ECC组件故障
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摘要
An apparatus comprises a check bit encoder circuit and a check/correct circuit. The apparatus operates on encoded data blocks, wherein each encoded data block includes a data block, a first plurality of check bits, and a second plurality of check bits. The encoded data block is logically arranged as an array of R rows and N columns, and each of the N columns comprises data bits from a respective one of the plurality of components. The first check bits form a first column of the array, and each of the first check bits covers a row of the array. The second 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 check vector corresponds to a different bit in the array and is an element of a Galois Field (GF(2R)). The check vectors are derived from a plurality of unique elements of GF(2R), each of which corresponds to a different column of the array. 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).
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机译:一种设备,包括校验位编码器电路和校验/校正电路。该设备对编码数据块进行操作,其中每个编码数据块包括数据块,第一多个校验位和第二多个校验位。编码数据块在逻辑上被布置为R行和N列的阵列,并且N列中的每一个包括来自多个组件中的各个组件的数据位。第一校验位形成阵列的第一列,并且每个第一校验位覆盖阵列的一行。第二校验位形成阵列的第二列,并且根据多个校验向量被定义为覆盖阵列中的位。每个校验向量对应于数组中的不同位,并且是伽罗瓦域(GF(2 R Sup>))的元素。校验向量是从GF(2 R Sup>)的多个唯一元素派生而来的,每个元素对应于数组的不同列。该列X行中的校验向量是该列唯一元素与GF(2 R Sup>)的乘积与alpha X Sup>的乘积,其中alpha是基元GF(2 R Sup>)的元素。
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