Performance curves for the non concatenated

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Unformatted text preview: decoder’s error events at its typical operating SNR. Figures 6-3 and 6-4 show the BER performance of the non-shortened (255,223) and (255,239) RS codes with E = 16 and E = 8, respectively, concatenated with punctured and non-punctured convolutional codes, with infinite interleaving assuming that interleaving produces independent RS symbol errors. Performance curves for the non-concatenated 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 Reed-Solomon 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 6-3: Performance of Concatenated Coding Systems with Infinite Interleaving, E=16, Punctured Codes CCSDS 130.1-G-1 Page 6-4 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 6-4: 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 6-5. Note that, in order to compare the performance of concatenated and non-concatenated codes, the Eb/N0 values on the x-axis 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 6-5 and 6-6 respectively for the recommended concatenated system consisting of the non-shortened (255,223) RS CCSDS 130.1-G-1 Page 6-5 June 2006 TM SYNCHRONIZATION AND CHANNEL CODING —SUMMARY OF CONCEPT AND RATIONALE code with E=16 and the non-punctured (7, 1/2) convolutional code, with different interleaving depths ranging from I = 1 to I = 16. Figure 6-5: Bit Error Rate Simulated Performance of the CCSDS Concatenated Scheme with Outer E=16 Reed-Solomon Code (255,223) and Inner Rate1/2 Convolutional Code as a Function of Interleaving Depth Figure 6-6: Word Error Rate Simulated Performance of the CCSDS Concatenated Scheme with Outer E=16 Reed-Solomon Code (255,223) and Inner Rate1/2 Convolutional Code as a Function of Interleaving Depth Figures 6-5 and 6-6 illustrate how interleaving depth I = 5 obtains near-ideal performance. This amount of interleaving is also sufficient to obtain near-ideal performance for most other combinations of recommended RS and convolutional codes. CCSDS 130.1-G-1 Page 6-6 June 2006 TM SYNCHRONIZATION AND CHANNEL CODING —SUMMARY OF CONCEPT AND RATIONALE Figures 6-7 and 6-8 show BER and WER for the recommended concatenated system consisting of the non-shortened (255,239) RS code with E = 8 and the non-punctured (7, 1/2) convolutional code, with different interleaving depths ranging from I = 1 to I = 16. Figure 6-7: Bit Error Rate Simulated Performance of the CCSDS Concatenated Scheme with Outer E=8 Reed-Solomon Code (255,239) and Inner Rate1/2 Convolutional Code as a Function of Interleaving Depth Figure 6-8: Word Error Rate Simulated Performance of the CCSDS Concatenated Scheme with Outer E=8 Reed-Solomon Code (255,239) and Inner Rate1/2 Convolutional Code as a Function of Interleaving Depth Figures 6-9 and 6-10 show BER and WER curves for the concatenated codes consisting of the non-shortened (255,223) RS code with E = 16 concatenated with any of the recommended punctured or non-punctured (7, 1/2) convolutional codes, with interleaving depth I = 5 (which gives a close approximation to ideal performance on the AWGN channel). CCSDS 130.1-G-1 Page 6-7 June 2006 TM SYNCHRONIZATION AND CHANNEL CODING —SUMMARY OF CONCEPT AND RATIONALE Figure 6-9: Bit Error Rate Simulated Performance of the CCSDS Concatenated Scheme with Outer E=16 Reed-Solomon Code (255,223) and Inner Punctured Convolutional Codes, Using Finite Interleaving with I=5 Figure 6-10:Word Error Rate Simulated Performance of the CCSDS Concatenated Scheme with Outer E=16 Reed-Solomon Code (255,223) and Inner Punctured Convolutional Codes, Using Finite Interleaving with I=5 Figures 6-11 and 6-12 show BER and WER curves for the concatenate...
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This document was uploaded on 03/06/2014.

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