Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Algebraic properties of BCH codes useful for decoding
AU - Cardoso Da Rocha, Valdemar
AU - Honary, Bahram
AU - Bate, Steve D.
PY - 1989
Y1 - 1989
N2 - In this paper theorems are presented which allow the simplified decoding of (n, k, δ) BCH codes in certain cases of practical interest. Such results are in a way implicit in the theory of BCH codes, but so far have not appeared explicitly in the literature. It is shown that any t0 errors, 1 ⩽ t0 ⩽ δ-1, can be detected by using any set of only t0 consecutive coefficients of the syndrome polynomial. The correction of any t0 errors, 1 ⩽ t0 ⩽ [(δ-1)/2], can be performed by using any set of 2t0 consecutive coefficients of the syndrome polynomial, where [x] means the integer part of x. Similar results are derived for punctured BCH codes. In this case sets of t0 or 2t0 consecutive coefficients, respectively, for detecting or correcting t0 errors, are selected from the δ-1-p higher-order coefficients of the modified syndrome polynomial, where p is the number of digits punctured from a code word. These results hold true even when the punctured digits are not consecutive.
AB - In this paper theorems are presented which allow the simplified decoding of (n, k, δ) BCH codes in certain cases of practical interest. Such results are in a way implicit in the theory of BCH codes, but so far have not appeared explicitly in the literature. It is shown that any t0 errors, 1 ⩽ t0 ⩽ δ-1, can be detected by using any set of only t0 consecutive coefficients of the syndrome polynomial. The correction of any t0 errors, 1 ⩽ t0 ⩽ [(δ-1)/2], can be performed by using any set of 2t0 consecutive coefficients of the syndrome polynomial, where [x] means the integer part of x. Similar results are derived for punctured BCH codes. In this case sets of t0 or 2t0 consecutive coefficients, respectively, for detecting or correcting t0 errors, are selected from the δ-1-p higher-order coefficients of the modified syndrome polynomial, where p is the number of digits punctured from a code word. These results hold true even when the punctured digits are not consecutive.
KW - Error detection and correction
KW - BCH codes
KW - Decoding
KW - Punctured codes
KW - Cyclic codes
U2 - 10.1002/sat.4600070313
DO - 10.1002/sat.4600070313
M3 - Journal article
VL - 7
SP - 225
EP - 229
JO - International Journal of Satellite Communications
JF - International Journal of Satellite Communications
SN - 1099-1247
IS - 3
ER -