130x1g2 - CCSDS

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TM SYNCHRONIZATION AND CHANNEL CODING—SUMMARY OF CONCEPT AND RATIONALE6.3 PERFORMANCE OF THE RECOMMENDED CONCATENATED CODINGSYSTEMSConsider a concatenated coding system consisting of a (K,r) convolutional inner code of rate rand constraint length K, and an (n,k) Reed-Solomon outer code. It is assumed that thesymbols are interleaved at a sufficient depth to insure that symbol errors are independent atthe RS decoder input. Then the bit, symbol, and word error probabilities, P b , P s , and P w ,respectively, are given by the formulas in the previous section, in terms of V s , the symbolerror probability at the input of the RS decoder or equivalently at the output of the Viterbidecoder, and V b, the bit error probability at the output of the Viterbi decoder. The ratio V b / V sis estimated empirically and depends on the burst statistics of the inner decoder’s error eventsat its typical operating SNR.Figures 6-3 and 6-4 show the BER performance of the non-shortened (255,223) andshortened (255,239) RS codes with E = 16 and E = 8, respectively, concatenated withpunctured and non-punctured convolutional codes, with ideal interleaving 5 assuming thatinterleaving produces independent RS symbol errors. Performance curves for the nonconcatenatedconvolutional codes and for the RS code alone are also shown for comparison.It should be noted that for bandwidth efficiency it is better to use concatenations of RS andpunctured convolutional codes than the Reed-Solomon code alone. Figure 6-5 shows theBER performance for both E=16 and E=8.5 Actually the value I=16 has been used as the semi‐analytical results are within 0.1 dB of fully simulated I=16results.<strong>CCSDS</strong> 130.1-G-2 Page 6-4 November 2012
TM SYNCHRONIZATION AND CHANNEL CODING—SUMMARY OF CONCEPT AND RATIONALEFigure 6-3: Performance of Concatenated Coding Systems with Ideal Interleaving,E=16, Punctured Codes<strong>CCSDS</strong> 130.1-G-2 Page 6-5 November 2012
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