130x1g2 - CCSDS

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TM SYNCHRONIZATION AND CHANNEL CODING—SUMMARY OF CONCEPT AND RATIONALE10 -210 -310 -410 -510 -1 E b /N o (dB)Block size = 1784 bits(Interleaving depth = 1)Cassini(15,1/6)+(255,223)Voyager(7,1/2)+(255,223)Turborate 1/6Turborate 1/3BER10 -6-0.50.00.51.01.52.02.53.03.5Figure 7-12: BER Performance of Turbo Codes Compared to Older CCSDS Codes(Except Cassini/Pathfinder Code: Reed-Solomon (255,223) + (15,1/6)Convolutional Code), Block Size 1784 Bits (Interleaving Depth = 1),Software Simulation, 10 IterationsFigure 7-13 compares the performance of the recommended Turbo codes of block length8920 bits and rates 1/3 and 1/6 with the performance of the Voyager and Cassini/Pathfinderconcatenated codes, now allowed to have interleaving depth I = 5 in order to produce equallengthframes of 8920 bits for all codes shown.CCSDS 130.1-G-2 Page 7-12 November 2012
TM SYNCHRONIZATION AND CHANNEL CODING—SUMMARY OF CONCEPT AND RATIONALE10 -410 -510 -1 E b/N o(dB)Turborate 1/6Turborate 1/3Block size = 8920 bits(Interleaving depth = 5)10 -2Cassini(15,1/6)+(255,223)Voyager(7,1/2)+(255,223)10 -3BER10 -6-0.50.00.51.01.52.02.5Figure 7-13: BER Performance of Turbo Codes Compared to Older CCSDS Codes(Except Cassini/Pathfinder Code: Reed-Solomon (255,223) + (15,1/6)Convolutional Code), Block Size 8920 Bits (Interleaving Depth = 5),Software Simulation, 10 Iterations7.4.3 THE TURBO DECODER ERROR FLOORAlthough Turbo codes can be found to approach the Shannon-limiting performance at verysmall required BERs, the Turbo code’s performance curve does not stay steep forever as doesthat of a convolutional/Reed-Solomon concatenated code. When it reaches the so-called‘error floor’, the curve flattens out considerably and looks from that point onward like theperformance curve for a weak convolutional code. In the error floor region, the weakness ofthe constituent codes takes charge, and the performance curve flattens out from that pointonward. The error floor is not an absolute lower limit on achievable error rate, but it is aregion where the slope of the Turbo code’s error rate curve becomes dramatically poorer.There exist transfer function bounds on Turbo code performance (reference [14]) thataccurately predict the actual Turbo decoder’s performance in the error floor region above theso-called ‘computational cutoff rate’ threshold, below which the bounds diverge and areuseless. More advanced bounds which are tight at lower values of bit SNR were developedin reference [29]. These bounds are computed from the code’s weight enumerator which isnot readily available for the recommended Turbo codes. Approximations valid in the errorfloor region can be obtained from considering only codewords of the lowest weight(s).Reference [30] gives a method for calculating the minimum distance of the recommendedCCSDS 130.1-G-2 Page 7-13 November 2012
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