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<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 D11.
Table D11. 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
104
105
106
___________________________________________________________________________
64 63 6.26x107 6.30x109 6.30x1011 56 55 5.47x107 5.50x109 5.50x1011 48 47 4.68x107 4.70x109 4.70x1011 40
39
3.89x107
3.90x109
3.90x1011
___________________________________________________________________________
Issue 6 Page D21 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  [(1p)n + (1p)np(1p)n1]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 + (1PTBF)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 maximumlength frames
organized into separate CLTUs (as shown in Figure D5) using SEC decoding mode, 64bit
codeblocks, channel BER of 105 and the fill bit algorithm is shown in Table D12.
Table D12: Example of Performance of Frames in First and
Second Contiguous CLTUs Using Fill Bit Algorithm
_______________________________________________________
PF2
Mode
PF1
_______________________________________________________
7.47x106
SEC
7.47x106
_______________________________________________________ Issue 6 Page D22 January 1987 CCSDS REPORT CONCERNING TELECOMMAND: SUMMARY OF CONCEPT AND SERVICE D5 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 109. 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 105 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 105, this will provide an undetected frame error rate of 1019 when using SEC
decoding; with TED decoding, the performance is better. Figure D7 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 105. These curves are from Reference [8]. Issue 6 Page D23 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 D7: Undetected Error Performance, With and
Without Cyclic Redundancy Code
END OF DOCUMENT. o Issue 6 Page D24 January 1987...
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