Circuitry and Method for Correcting 3-bit Errors Containing Adjacent 2-Bit Error

摘要

A circuitry is proposed for the correction of errors in a possibly erroneous binary word v′=v′1, . . . , v′n relative to a codeword v=v1, . . . , vn, in particular 3-bit errors containing an adjacent 2-bit error (burst error). The circuitry comprises a syndrome generator and a decoder. A modified BCH is used wherein n′ column vectors of a first BCH code submatrix are paired as column vector pairs so that a componentwise XOR combination of the two column vectors of each column vector pair produces an identical column vector K that is different from all column vectors of the first BCH submatrix. A second BCH submatrix comprises corresponding column vectors as the third power, according to Galois field arithmetic, of the column vector in the first BCH submatrix. The syndrome generated by the syndrome generator can be checked against the columns of the first and second submatrices.

主权项

1. A circuitry for the correction of errors in a possibly erroneous binary word v′=v′1, . . . , v′n relative to a codeword v=v1, . . . , vn, the circuitry comprising:
a syndrome generator for determining an error syndrome s=(s1, s3) according to a modified BCH code with a H-matrix Hmod comprising a first BCH submatrix H1mod and a second BCH submatrix H3mod, and with a code distance d≧5,
wherein n′ column vectors of the BCH submatrix H1mod are paired as column vector pairs so that a componentwise XOR combination of the two column vectors of each column vector pair produces an identical column vector K that is different from all column vectors of the first BCH submatrix H1mod and where n′ is even and 4≦n′≦n applies,wherein the second BCH submatrix H3mod comprises a corresponding column vector for each column vector in the first BCH submatrix H1mod so that the corresponding column vector is the third power, according to Galois field arithmetic, of the column vector in the first BCH submatrix H1mod, wherein the syndrome generator is configured to determine the error syndrome s by multiplying the H-matrix Hmod with the possibly erroneous binary word v′ so that a first error syndrome portion is given by s1=H1mod·v′ and a second error syndrome portion is given by s3=H3mod·v′; and a decoder for generating a correction vector e=(e1, . . . , en) with correction values ej=ej+1=el=1 and et=0 for t≠j, j+1, l, if the first error syndrome portion s1 equals the component-wise XOR combination of the identical column vector K and a column vector at a column position l of the first BCH submatrix H1mod, and if the second error syndrome portion s3 equals the componentwise XOR combination of column vectors at column positions j, j+1, and l of the second BCH submatrix H3mod.