That is two changes have to occur in the same

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Unformatted text preview: osition. <Prob. of missing a tail sequence using fill bit test> = [1 - (1 - p)n]p = PTBF [EQ. M] Comparing this with Equation H, one can see that the probability of missing a tail sequence has now been reduced by several orders of magnitude (i.e., by the bit error rate, p.) Values are given in Table D-11. Table D-11. Probability of Missing a Tail Sequence, P TBF , Using the Fill Bit Algorithm (SEC Decoding Mode Only) ___________________________________________________________________________ Probability of missing tail sequence Codeblock n, for channel BER of length, bits bits 10-4 10-5 10-6 ___________________________________________________________________________ 64 63 6.26x10-7 6.30x10-9 6.30x10-11 56 55 5.47x10-7 5.50x10-9 5.50x10-11 48 47 4.68x10-7 4.70x10-9 4.70x10-11 40 39 3.89x10-7 3.90x10-9 3.90x10-11 ___________________________________________________________________________ Issue 6 Page D-21 January 1987 CCSDS REPORT CONCERNING TELECOMMAND: SUMMARY OF CONCEPT AND SERVICE It should be noted that while this technique substantially reduces the likelihood of missing a tail sequence, there is a penalty in the form of a slight increase in frame rejection rate. That is, a codeblock containing one error which would normally be corrected and accepted may (but rarely) also have an error in its fill bit. If this algorithm were not used, the erroneous fill bit would not be tested and the codeblock would be accepted. Under this algorithm, such a codeblock would be rejected even though the information was correctable. The equation for codeblock rejection (PCB, Equation D) must be modified to account for testing the fill bit (as shown for PCBF, Equation N) but the effect on codeblock rejection is very slight: <Prob. of codeblock rejection, SEC mode and using fill bit test> = PCBF (fill bit test) = 1 - [(1-p)n + (1-p)np(1-p)n-1]N [EQ. N] Frame rejection performance for the frame in the second CLTU is then: <Prob. of last frame rejection in subsequent CLTU, using SEC decoding and the fill bit algorithm> = PF2BF = PTBF + (1-PTBF)PFBF [EQ. O] where PTBF = prob. of missing tail when using fill bit test (Equation M) PFBF = PSB + (1 - PSB)PCBF and PCBF = prob. of codeblock rejection when using fill bit test (Equation N) Example. The probability of frame rejection for the example of two maximum-length frames organized into separate CLTUs (as shown in Figure D-5) using SEC decoding mode, 64-bit codeblocks, channel BER of 10-5 and the fill bit algorithm is shown in Table D-12. Table D-12: Example of Performance of Frames in First and Second Contiguous CLTUs Using Fill Bit Algorithm _______________________________________________________ PF2 Mode PF1 _______________________________________________________ 7.47x10-6 SEC 7.47x10-6 _______________________________________________________ Issue 6 Page D-22 January 1987 CCSDS REPORT CONCERNING TELECOMMAND: SUMMARY OF CONCEPT AND SERVICE D-5 UNDETECTED ERROR PERFORMANCE The second performance requirement deals with undetected error, and requires that the probability of accepting a frame with an undetected error is greater than 10-9. Again, the unit of accountability is the frame. Often the methods used to improve frame rejection rate (such as SEC) cause reduced performance on undetected errors, and vice versa. Therefore an acceptable balance must be found between these two objectives. Reference [8] shows that the required undetected error performance will be met by the prescribed system using either TED or SEC decoding in a channel operating at a BER of 10-5 without extra precautions. However, if a greater margin of safety against undetected errors is desired, the cyclic redundancy code specified in Reference [8] may be added to each frame. For an overhead of 16 bits per frame and the same channel BER of 10-5, this will provide an undetected frame error rate of 10-19 when using SEC decoding; with TED decoding, the performance is better. Figure D-7 shows curves comparing undetected error performance (with and without the added CRC) as a function of number of codeblocks in a frame for channel BER of 10-5. These curves are from Reference [8]. Issue 6 Page D-23 January 1987 CCSDS REPORT CONCERNING TELECOMMAND: SUMMARY OF CONCEPT AND SERVICE 10 -09 (SEC DECODING) PROBABILITY OF UNDETECTED FRAME ERROR 10 -10 10 -11 BCH CODEBLOCKS ALONE 10 -14 10 -15 (TED DECODING) 10 -16 10 -19 10 -20 BCH CODEBLOCKS CONCATENATED WITH FRAME CRC (SEC DECODING) 10 -21 10 -22 0 10 20 30 40 50 60 NUMBER OF CODEBLOCKS PER FRAME Figure D-7: Undetected Error Performance, With and Without Cyclic Redundancy Code END OF DOCUMENT. o Issue 6 Page D-24 January 1987...
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This document was uploaded on 03/06/2014.

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