Unformatted text preview: decoder’s error events
at its typical operating SNR.
Figures 63 and 64 show the BER performance of the nonshortened (255,223) and
(255,239) RS codes with E = 16 and E = 8, respectively, concatenated with punctured and
nonpunctured convolutional codes, with infinite interleaving assuming that interleaving
produces independent RS symbol errors. Performance curves for the nonconcatenated
convolutional codes and for the RS code alone are also shown for comparison. Note that for
bandwidth efficiency it is better to use concatenations of RS and punctured convolutional
codes than the ReedSolomon code alone.
10 1 convolutional
conv.+RS (255,223)
10 2 E=16 10 4 BER 10 3 uncoded
10 5 3/4 10 6 1/2
RS (255,223)
10 1/2*
0.437
10 7/8 0.874 7 3/4*
0.656 7/8*
0.765 8 0 1 2 3 4 5 6 7 8 9 10 11 Eb/No (dB) Figure 63: Performance of Concatenated Coding Systems with Infinite Interleaving,
E=16, Punctured Codes CCSDS 130.1G1 Page 64 June 2006 TM SYNCHRONIZATION AND CHANNEL CODING —SUMMARY OF CONCEPT AND RATIONALE 10 1 convolutional
conv.+RS (255,239)
10 2 E=8 10 4 BER 10 3 uncoded
10 5 3/4
1/2
10 6 7/8
10 7 3/4* 1/2*
0.469
10 0.703 3 4 7/8*
0.82 RS (255,239)
0.937 8 0 1 2 5 6 7 8 9 10 11 Eb /No (dB) Figure 64: Performance of Concatenated Coding Systems with Infinite Interleaving,
E=8, Punctured Codes
The convolutional decoder used to calculate the performance curves for all of the figures in
this section operated with an unquantized maximum likelihood soft decision algorithm,
corresponding to the ‘unquantized soft decision’ curve in figure 65. Note that, in order to
compare the performance of concatenated and nonconcatenated codes, the Eb/N0 values on
the xaxis in all figures in this section refer to the information bit SNR.
Effects of Finite Interleaving — When the interleaving depth I is not large enough, the
errors at the output of the Viterbi decoder cannot be considered as independent since this
decoder tends to produce errors in bursts. The performance under finite interleaving must
therefore take into account the statistics of these bursts either by devising a plausible model
or by simulation. A possible model for burst lengths and arrival times was developed
in reference [27] and is called the geometric model. This model provides an approximate
estimate of the performance under finite interleaving, but ignores the actual structure of the
error patterns within the bursts. On the other hand, simulation is also problematic since very
large amounts of Viterbi decoded data is necessary to provide reasonable confidence in the
estimates of performance. A detailed description of methods to obtain performance estimates
is given in reference [28].
BER and WER results for finite interleaving are shown in figures 65 and 66 respectively
for the recommended concatenated system consisting of the nonshortened (255,223) RS CCSDS 130.1G1 Page 65 June 2006 TM SYNCHRONIZATION AND CHANNEL CODING —SUMMARY OF CONCEPT AND RATIONALE code with E=16 and the nonpunctured (7, 1/2) convolutional code, with different
interleaving depths ranging from I = 1 to I = 16. Figure 65: Bit Error Rate Simulated Performance of the CCSDS Concatenated
Scheme with Outer E=16 ReedSolomon Code (255,223) and Inner Rate1/2 Convolutional Code as a Function of Interleaving Depth Figure 66: Word Error Rate Simulated Performance of the CCSDS Concatenated
Scheme with Outer E=16 ReedSolomon Code (255,223) and Inner Rate1/2 Convolutional Code as a Function of Interleaving Depth
Figures 65 and 66 illustrate how interleaving depth I = 5 obtains nearideal performance.
This amount of interleaving is also sufficient to obtain nearideal performance for most other
combinations of recommended RS and convolutional codes. CCSDS 130.1G1 Page 66 June 2006 TM SYNCHRONIZATION AND CHANNEL CODING —SUMMARY OF CONCEPT AND RATIONALE Figures 67 and 68 show BER and WER for the recommended concatenated system
consisting of the nonshortened (255,239) RS code with E = 8 and the nonpunctured (7, 1/2)
convolutional code, with different interleaving depths ranging from I = 1 to I = 16. Figure 67: Bit Error Rate Simulated Performance of the CCSDS Concatenated
Scheme with Outer E=8 ReedSolomon Code (255,239) and Inner Rate1/2 Convolutional Code as a Function of Interleaving Depth Figure 68: Word Error Rate Simulated Performance of the CCSDS Concatenated
Scheme with Outer E=8 ReedSolomon Code (255,239) and Inner Rate1/2 Convolutional Code as a Function of Interleaving Depth
Figures 69 and 610 show BER and WER curves for the concatenated codes consisting of
the nonshortened (255,223) RS code with E = 16 concatenated with any of the recommended
punctured or nonpunctured (7, 1/2) convolutional codes, with interleaving depth I = 5 (which
gives a close approximation to ideal performance on the AWGN channel). CCSDS 130.1G1 Page 67 June 2006 TM SYNCHRONIZATION AND CHANNEL CODING —SUMMARY OF CONCEPT AND RATIONALE Figure 69: Bit Error Rate Simulated Performance of the CCSDS Concatenated
Scheme with Outer E=16 ReedSolomon Code (255,223) and Inner
Punctured Convolutional Codes, Using Finite Interleaving with I=5 Figure 610:Word Error Rate Simulated Performance of the CCSDS Concatenated
Scheme with Outer E=16 ReedSolomon Code (255,223) and Inner
Punctured Convolutional Codes, Using Finite Interleaving with I=5
Figures 611 and 612 show BER and WER curves for the concatenate...
View
Full Document
 Spring '14
 Information Theory, ........., Error detection and correction, CCSDS

Click to edit the document details