The performance gains achieved by the corresponding

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Unformatted text preview: s standard codes 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 in figures 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 length 1784 bits and rates 1/3 and 1/6 with the performance of the CCSDS concatenated code used by Voyager and that of the non-CCSDS concatenated code used by Cassini and Mars Pathfinder. 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 code consists of the same Reed-Solomon code concatenated with a (15, 1/6) convolutional code for which the Viterbi decoder requires 28 = 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, not the actual interleaving depths used in the Voyager/Cassini/Pathfinder missions, in order to provide a fair comparison with the performance of the two turbo codes with block length 1784. In other words, a frame length of 1784 bits is assumed for all four curves in this figure. CCSDS 130.1-G-1 Page 7-11 June 2006 TM SYNCHRONIZATION AND CHANNEL CODING —SUMMARY OF CONCEPT AND RATIONALE 10 -1 Block size = 1784 bits (Interleaving depth = 1) 10 Turbo rate 1/6 Turbo rate 1/3 -3 BER 10 Voyager (7,1/2)+(255,223) Cassini (15,1/6)+(255,223) -2 10 10 10 -4 -5 -6 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 E b /No (dB) Figure 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 Iterations Figure 7-13 compares the performance of the recommended turbo codes of block length 8920 bits and rates 1/3 and 1/6 with the performance of the Voyager and Cassini/Pathfinder concatenated codes, now allowed to have interleaving depth I = 5 in order to produce equallength frames of 8920 bits for all codes shown. CCSDS 130.1-G-1 Page 7-12 June 2006 TM SYNCHRONIZATION AND CHANNEL CODING —SUMMARY OF CONCEPT AND RATIONALE 10 -1 Turbo rate 1/6 10 Block size = 8920 bits (Interleaving depth = 5) Turbo rate 1/3 -2 Voyager (7,1/2)+(255,223) Cassini (15,1/6)+(255,223) -3 BER 10 10 10 10 -4 -5 -6 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 E b /No (dB) Figure 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 Iterations 7.4.3 THE TURBO DECODER ERROR FLOOR Although turbo codes can be found to approach the Shannon-limiting performance at very small required bit error rates, the turbo code’s performance curve does not stay steep forever as does that of a convolutional/Reed-Solomon concatenated code. When it reaches the socalled ‘error floor’, the curve flattens out considerably and looks from that point onward like the performance curve for a weak convolutional code. In the error floor region, the weakness of the constituent codes takes charge, and the performance curve flattens out from that point onward. The error floor is not an absolute lower limit on achievable error rate, but it is a region where the slope of the turbo code’s error rate curve becomes dramatically poorer. There exist transfer function bounds on turbo code performance (reference [15]) that accurately predict the actual turbo decoder’s performance in the error floor region above the so-called ‘computational cutoff rate’ threshold, below which the bounds diverge and are useless. More advanced bounds which are tight at lower values of bit SNR were developed in reference [29]. These bounds are computed from the code’s weight enumerator which is not readily available for the recommended turbo codes. Approximations valid in the error floor 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 recommended CCSDS 130.1-G-1 Page 7-13 June 2006 TM SYNCHRONIZATION AND CHANNEL CODING —SUMMARY OF CONCEPT AND RATIONALE codes and the corresponding estimates of BER on the error floor. Other details on algorithms for computing CCSDS turbo code minimum distance and error floors can be found in reference [32]. Figure 7-14 provides an illustration of the transition of a turbo code performance curve from a steep ‘waterfall’ region into a much flatter ‘error floor’ region for two turbo codes analyzed as an example. This figure shows the actual simulated turbo code performance compared with bounds approximating the error floor. The original turbo codes of Berrou et al. (reference [17]) had error floors starting at a BER of about 10-5. By using theoretical pre...
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This document was uploaded on 03/06/2014.

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