| 主权项 |
1. A computer-implemented method for systematic decoding of an information vector for use in correction of all asymmetric errors of maximum magnitude l and executed by a processor, comprising:
a) providing a q-ary encoded vector that includes an information vector having k received information digits, (x′k-1, x′k-2, . . . , x′0) and having received check symbols (c′r-1, c′r-2, . . . , c′0), wherer≥k×log(l+1)log⌈ql+1⌉; b) recovering the check symbols (cr-1, cr-2, . . . , c0) by rounding each received check symbol which is not a multiple of (l+1) upwards to the nearest multiple of (l+1); c) computing a, the value of(cr-1l+1,cr-2l+1,…,c0l+1) as a vector overZ⌈ql+1⌉ asa=(cr-1l+1)⌈ql+1⌉r-1+(cr-2l+1)⌈ql+1⌉r-2+…+(c0l+1)⌈ql+1⌉0; d) representing a in radix (l+1) number with k digits as y=(yk-1,yk-2, . . . ,y0); e) computing ei=(yi−x′i) mod(l+1); and f) computing the corrected codeword, (xk-1, xk-2, . . . , x0), as xi=x′i+ei, where i=0, 1, . . . , k-1. |
