# Codeblock as used here refers to the physical

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Unformatted text preview: ) code, the codeword is always n bits long. "Codeblock" as used here refers to the physical implementation in the bit stream and includes the final fill bit. Codeblocks may be 40, 48, 56 or 64 bits in length. Issue 6 Page D-8 January 1987 CCSDS REPORT CONCERNING TELECOMMAND: SUMMARY OF CONCEPT AND SERVICE The equation characterizing codeblock rejection using TED mode is: <Prob. of 1 or more codeblocks of the CLTU being detected as in error (using TED mode)> = PCA = 1 - [1 - p)n]N [EQ. C] where p = channel bit error rate n = number of bits in codeword (1 less than codeblock) N = number of codeblocks For the SEC case, the equation for rejection of 1 or more codeblocks becomes: <Prob. of 1 or more codeblock of the CLTU being in error AND UNCORRECTABLE (SEC mode)> = PCB = 1 - [(1-p)n + np(1-p)n-1]N [EQ. D] Table D-3 provides values for both PCA and PCB for different numbers of 64-bit codeblocks for the three different channel error rates, and these values are plotted in Figure D-2. The codeblock factor is the second factor affecting frame rejection performance. Performance is discussed next. Issue 6 Page D-9 January 1987 CCSDS REPORT CONCERNING TELECOMMAND: SUMMARY OF CONCEPT AND SERVICE Table D-3: Probability of Codeblock Rejection (for 64-bit codeblocks, n=63) as a Function of Number of Codeblocks, N N BER = 10-4 BER = 10-5 BER = 10-6 P CA (TED mode) 1 2 4 6 9 12 16 20 24 28 32 36 37 74 110 149 6.28 1.25 2.49 3.71 5.51 7.28 9.59 1.18 1.40 1.62 1.83 2.03 2.08 3.73 5.00 6.09 x x x x x x x x x x x x x x x x 10-3 10-2 10-2 10-2 10-2 10-2 10-2 10-1 10-1 10-1 10-1 10-1 10-1 10-1 10-1 10-1 6.30 1.26 2.52 3.77 5.65 7.53 1.00 1.25 1.50 1.74 2.00 2.24 2.30 4.56 6.70 8.96 x x x x x x x x x x x x x x x x 10-4 10-3 10-3 10-3 10-3 10-3 10-2 10-2 10-2 10-2 10-2 10-2 10-2 10-2 10-2 10-2 6.30 1.26 2.52 3.78 5.67 7.56 1.01 1.26 1.51 1.76 2.01 2.27 2.33 4.65 6.91 9.34 x x x x x x x x x x x x x x x x 10-5 10-4 10-4 10-4 10-4 10-4 10-3 10-3 10-3 10-3 10-3 10-3 10-3 10-3 10-3 10-3 1.95 3.91 7.81 1.17 1.76 2.34 3.12 3.91 4.69 5.47 6.25 7.03 7.23 1.45 2.15 2.91 x x x x x x x x x x x x x x x x 10-9 10-9 10-9 10-8 10-8 10-8 10-8 10-8 10-8 10-8 10-8 10-8 10-8 10-7 10-7 10-7 P CB (SEC mode) 1 2 4 6 9 12 16 20 24 28 32 36 37 74 110 149 Issue 6 1.95 3.90 7.78 1.17 1.75 2.33 3.11 3.89 4.67 5.44 6.22 7.00 7.19 1.44 2.14 2.89 x x x x x x x x x x x x x x x x 10-5 10-5 10-5 10-4 10-4 10-4 10-4 10-4 10-4 10-4 10-4 10-4 10-4 10-3 10-3 10-3 1.95 3.90 7.81 1.17 1.76 2.34 3.12 3.90 4.69 5.47 6.25 7.03 7.22 1.44 2.15 2.91 Page D-10 x x x x x x x x x x x x x x x x 10-7 10-7 10-7 10-6 10-6 10-6 10-6 10-6 10-6 10-6 10-6 10-6 10-6 10-5 10-5 10-5 January 1987 CCSDS REPORT CONCERNING TELECOMMAND: SUMMARY OF CONCEPT AND SERVICE PROBABILITY OF REJECTION OF ONE OR MORE CODEBLOCKS 10-0 P CA , USING , TED 10-1 BER = 10-4 BER = 10-5 10-2 BER = 10-6 10-3 BER = 10-4 10-4 10-5 BER = 10-5 10-6 P CB , USING SEC 10-7 BER = 10-6 10-8 10-9 0 10 20 30 40 50 60 NUMBER OF CODEWORDS PER FRAME, N (BASED ON 64-BIT CODEBLOCKS) Figure D-2: Probability of Rejection of One or More Contiguous 64-Bit Codeblocks as a Function of Number of Codeblocks, N Issue 6 Page D-11 January 1987 CCSDS REPORT CONCERNING TELECOMMAND: SUMMARY OF CONCEPT AND SERVICE D-4 FRAME REJECTION RATE: TYPICAL TC ORGANIZATIONS The Telecommand Transfer Frame is the accounting entity for telecommand performance....
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