Циклические коды. CRC и БЧХ коды

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. CRC . . . . ** . ** CRC . -- CRC . . -- CRC. - PowerPoint PPT Presentation

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<p> . CRC .</p> <p> . CRC . . ** CRC -- CRC-- -- . ** -- CRC . -- ** ** * - , . </p> <p>* q . , ( 1), (q = 2).* . . </p> <p>* Vk - VJ : ( ) .* - , - CRC, , - ..CRC . ** Cyclic Redundancy Code (CRC) **</p> <p>* CRC , , , . </p> <p>* CRC .* , , . CRC32 2-32.* , , , ; CRC. </p> <p>* (, ), : 9/3=3, = 0; (9+2)/3=3, = 2.* CRC , " ". "" .</p> <p>* "" . " " (eXclusive OR, - XOR), .</p> <p>* CRC-:</p> <p> CRC* CRC , . (W Width) , , 1001 "3", "4". </p> <p>* , 1, , , , .</p> <p>: 1101011011111 2 : 1. XOR , 1, . 2. XOR W , 0. * : . , . </p> <p>* , , , . . * , . , , (11,7) 7- ASCII-. </p> <p>* , 7- 4 (7+4=11). , .* , . . , ( , , 4):* 00000111 , 00001111. .</p> <p>* s = 0x073 = 1110011 (11,7).</p> <p>* * , . 2 (1, 2, 4, 8 ..). </p> <p>* XOR ( ) . 11, 10, 9, 5 3. :</p> <p>* , :</p> <p>* :</p> <p>* , , 7 (1 0) 5 (0 1). .</p> <p>* N=M+C , . N+1 ( n ). =4, N=7, - : M4, M3, M2, C3, M1, C2, C1. 1, 2, 3. , 2:</p> <p>* , , ( 2):</p> <p>* :</p> <p>* n . n , N . , . * , . , qm.* , qmm ( , D = 2qm + 1). N n- D.</p> <p>* . k , k=n - log2(n+1), ( 2), k 0, 1, 4, 11, 26, 57 .., (3,1); (7,4); (15,11); (31,26); (63,57) ... . ** - - (-) , . **</p> <p>* , , .</p> <p>* -- () , , . . (d0 &gt;= 5).* - .</p> <p>* - , - .* - , , - P(). </p> <p>* n S, - k .* . </p> <p>* - GF(q), q . </p> <p>* , q = 2.* g(x) , n (n = 2m - 1), , , 2m.* :</p> <p> ((r1()) g(x) r1(). </p> <p>* . 2m , GF(2m) m GF(2m). (1) (0).* . 2m , GF(2m) m GF(2m). (1) (0).</p> <p>* , (ra()) (ra()), :</p> <p> * - - , - , . </p> <p>* . * - GF(2m), - - g(x) m, n = 2m - 1. * s </p> <p>* . . , . ,</p> <p>* , :</p> <p>* 3- 4- . .. , . .* . </p> <p>* , , :</p> <p>* , , .</p> <p>* :</p> <p>* :</p> <p>* :</p> <p>* - () :</p> <p>* , n = 15, , :</p> <p>* .** : 15- , (. . n = 15, S = 2) **</p> <p>: m k m </p>