130x1g2 - CCSDS

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BER & FERTM SYNCHRONIZATION AND CHANNEL CODING—SUMMARY OF CONCEPT AND RATIONALEFigure 7-10 shows the simulated performance of Turbo codes of rates 1/2, 1/3, 1/4, and 1/6with an information block length of 16384 bits. These performance curves do not necessarilyreflect the performance of the CCSDS codes for this block length since the recommendedinterleaver for this block length has not been specified yet.10 -310 -410 -610 0 E b /N o (dB)Bock size = 1638410 -110 -2FERBERrate 1/3rate 1/6rate 1/210 -5rate 1/410 -710 -8-0 .4-0 .3-0 .2-0 .1-0 .00.10.20.30.40.50.60.70.80.91.01.11.2Figure 7-10: BER and FER Performance for Rate 1/2, 1/4, 1/3 and 1/6 Turbo Codes,Block Size 16384 Bits, Software Simulation, 10 IterationsFigure 7-11 illustrates how the decoder’s average speed can be increased through the use ofstopping rules.Speed (Kbps)1000800600400Frame Error Rate = 10 -489201/617841/689201/317841/317841/233.33.754.3567.5Average Number of Iterations10 iterations fixed10200-0.5 0 0.5 1 1.5 2 2.5E b /N o (dB)15Figure 7-11: Illustration of Decoder Speedup Using Stopping RulesCCSDS 130.1-G-2 Page 7-10 November 2012
TM SYNCHRONIZATION AND CHANNEL CODING—SUMMARY OF CONCEPT AND RATIONALEThe x-axis shows the threshold value of E b /N 0 required to reach a FER of 10 -4 . The y-axisshows the average decoding speed, or reciprocally the average number of iterations. In thisfigure a decoder using a fixed 10 iterations achieves a speed of 300 Kb/s, and the decoder’saverage speed increases inversely as the average number of iterations is reduced byapplication of the stopping rule. The results in this figure are for a selection of recommendedTurbo codes with block lengths 1784 and 8920. The figure shows that effective stoppingrules can increase the decoder speed on the order of 50% to 100% with virtually nocompromise in the required value of E b /N 0 ; further increases in speed can also be obtained bytrading off additional SNR for increased speed.7.4.2 COMPARISON TO TRADITIONAL CONCATENATED CODESTurbo codes gain a significant performance improvement over the traditional Reed-Solomonand convolutional concatenated codes currently recommended by CCSDS. For example, toachieve an overall BER of 10 -6 with a block length of 8920 bits (depth-5 interleaving), therequired bit-SNRs are approximately 0.8 dB, 1.0 dB, and 2.6 dB for the DSN’s standardcodes consisting of the (255,223) Reed-Solomon code concatenated with the (15,1/6)convolutional code, the (15,1/4) convolutional code, and the (7,1/2) convolutional code,respectively. The performance gains achieved by the corresponding-rate Turbo codes infigures 7-6, 7-7, 7-8, 7-9, and 7-10 range from 0.9 dB to 1.6 dB.Figure 7-12 compares the performance of the recommended Turbo codes of block length1784 bits and rates 1/3 and 1/6 with the performance of the CCSDS concatenated code usedby Voyager and that of the non-CCSDS concatenated code used by Cassini and MarsPathfinder. The Voyager code consists of the recommended concatenation of the (255, 223)Reed-Solomon code with the (7,1/2) convolutional code. The Cassini/Pathfinder codeconsists of the same Reed-Solomon code concatenated with a (15, 1/6) convolutional codefor which the Viterbi decoder requires 2 8 = 256 times as many states as for the (7, 1/2) code.Performance for both concatenated codes is obtained using an interleaving depth of I = 1, notthe actual interleaving depths used in the Voyager/Cassini/Pathfinder missions, in order toprovide a fair comparison with the performance of the two Turbo codes with block length1784. In other words, a frame length of 1784 bits is assumed for all four curves in this figure.CCSDS 130.1-G-2 Page 7-11 November 2012
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