130x1g2 - CCSDS

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TM SYNCHRONIZATION AND CHANNEL CODING—SUMMARY OF CONCEPT AND RATIONALEsizes ranging from 256 to 49152 information bits. Similar results were obtained for Turbocodes in the same family with rates 1/2, 1/4, and 1/6. The significance of these results is thatTurbo codes appear to be uniformly good over the entire span of block sizes shown,including all of the CCSDS recommended block lengths. The bound is plotted forWER=1e-4, while the Turbo code performance is plotted for BER=1e-6. While betterconsistency could be achieved if Turbo code performance data were available at WER=1e-4,experience shows that for a rate 1/3 Turbo code operating under these conditions, the BERand WER curves are separated by about two orders of magnitude. Moreover, the BER andWER curves are steep, so the threshold Eb/No is not very sensitive to the error rate criterionused.5Threshold Eb/No (dB)43210Turbo r=1/3Bound r=1/3-110 100 1000 10000 100000Information Block Size (bits)NOTE – Bound is calculated for WER of 10 –4 , while Turbo code simulations were forBER of 10 –6 .Figure D-1: Comparison of Turbo Code Performance with Block Length-ConstrainedLower BoundD4CONSTITUENT CODESEffective Turbo codes can be constructed from a wide variety of constituents. Here are someof the factors underlying the choice of constituent codes that led to the recommendedCCSDS Turbo codes.Number and Type of Constituent Codes — Turbo codes with more than two constituentcodes are feasible in principle, but to this point they have not been well studied — mainlybecause two-component Turbo codes already perform so well. The best performing and bestunderstood constituent codes discovered thus far are the class of recursive convolutionalcodes, as recommended in 7.2 and in the original Turbo code paper by Berrou, et al.CCSDS 130.1-G-2 Page D-2 November 2012
TM SYNCHRONIZATION AND CHANNEL CODING—SUMMARY OF CONCEPT AND RATIONALEConstraint Length — The recommended Turbo code is formed from two recursiveconvolutional codes with constraint length K = 5. Higher constraint lengths are more complexto decode, and they seem to offer negligible performance improvement. In the otherdirection, constituent codes with constraint lengths less than 5 sacrifice some performance toachieve higher decoding speeds.Code Generator Polynomials — Considerable theory has been developed to guide thechoice of constituent code generator polynomials. This theory is based on the transferfunction bounds that are used to predict the Turbo decoder error floor. The error floor can belowered the most if the divisor polynomial (G0 in figure 7-3) is a primitive polynomial.Additional theoretical considerations guide the choice of the remaining polynomials.Code Transparency — Turbo codes are inherently non-transparent, meaning that thecomplement of a codeword is not a codeword (or equivalently, the all-‘ones’ sequence is nota codeword). However, a Turbo code can be made ‘approximately transparent’ except nearthe edges of the codeword. It is a system design issue to decide whether an approximatelytransparent Turbo code would be preferred, at some sacrifice of performance, to onedesigned without any transparency constraints. The Turbo codes in the RecommendedStandard (reference [3]) are not constructed to be approximately transparent.D5PERMUTATIONThe (analytically) best-understood permutations for Turbo codes are completely random. Thebest-performing permutations are manually optimized for each block size, and they also lookvery random. Manually optimized permutations generally outperform purely randompermutations by only a small amount, except that they may significantly lower the errorfloor. However, such a permutation needs to be stored in ROM as a lookup table, because itis infeasible to recompute it on the fly for every codeword. The permutation in theRecommended Standard (reference [3]) can be generated on-the-fly by applying a simplerule. It also looks very random and performs nearly as well (within 0.1 dB, see figure D-2) asthe manually optimized permutation. The recommended permutation gives the implementeran option to calculate the permutation on-the-fly in preference to using a look-up table. Itmay be noted that a simple rectangular interleaver, such as the interleaver recommended forReed-Solomon codes (see 5.3), is not suitable for Turbo codes.The interpretation of the permutation numbers in the Recommended Standard (reference [3])is such that the sth bit read out on line ‘in b’ (in figure 7-3) is the π(s)th bit of the inputinformation block, as shown in figure D-3.D6SOME SYSTEM ISSUES PERTINENT TO THE USE OF TURBO CODESLower symbol SNR — To take advantage of the improved performance of Turbo codes, thereceiving system must operate at a significantly lower symbol signal-to-noise ratio (SSNR)than that of a less powerful code with the same code rate. This imposes more stringent demandsCCSDS 130.1-G-2 Page D-3 November 2012
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