# and row 8 in t l are polynomials in corresponding to

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Unformatted text preview: 0 0 1 0 0 1 0 1 0 0 -1 Row 1, row 2, ... , and row 8 in Tα l are polynomials in ‘α’ corresponding to l0 (10 ... 0), l1 (010 ... 0), ... , and l7 (00, ... 01), respectively. -1 [z0, z1, ... , z7 ] Tα l Thus, = [u7, u6, ... , u0] Example 1: Given information symbol I, [z0, z1, ... , z7] = 10111001 then T [1 0 1 1 1 0 0 1] 1 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 1 1 0 0 0 0 1 1 1 0 0 -1 0 0 1 1 0 1 1 1 1 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 0 = [u7, u6, ..., u0] = 00101010 = I' The arithmetic operations are reduced modulo 2. Also, [z0, z1, ... , z7] = 10111001 and [u7, u6, ... , u0] = 00101010 (α213) are corresponding entries in table F-1. CCSDS 131.0-B-2 Page F-3 August 2011 CCSDS RECOMMENDED STANDARD FOR TM SYNCHRONIZATION AND CHANNEL CODING Example 2: Given check symbol C ', [α7, α6, ..., α0] = 01011001 (α152) Then, [0 1 0 1 1 0 0 1] CCSDS 131.0-B-2 1 1 1 1 1 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 1 1 0 1 1 1 1 0 0 0 1 1 1 = [z 0, z 1, ..., z 7] = 11101000 = C Page F-4 August 2011 CCSDS RECOMMENDED STANDARD FOR TM SYNCHRONIZATION AND CHANNEL CODING Table F-1: Equivalence of Representations 1 P O W E R POLY IN ALPHA P O W E R l01234567 =================== ============= * 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 00000000 00000001 00000010 00000100 00001000 00010000 00100000 01000000 10000000 10000111 10001001 10010101 10101101 11011101 00111101 01111010 11110100 01101111 11011110 00111011 01110110 11101100 01011111 10111110 11111011 01110001 11100010 01000011 10000110 10001011 10010001 10100101 POLY IN ALPHA l01234567 =================== ============= 00000000 01111011 10101111 10011001 11111010 10000110 11101100 11101111 10001101 11000000 00001100 11101001 01111001 11111100 01110010 11010000 10010001 10110100 00101000 01000100 10110011 11101101 11011110 00101011 00100110 11111110 00100001 00111011 10111011 10100011 01110000 10000011 31 32 33 34 35 36...
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## This document was uploaded on 03/06/2014.

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