130x1g2 - CCSDS

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TM SYNCHRONIZATION AND CHANNEL CODING—SUMMARY OF CONCEPT AND RATIONALEFigure 6-1: Concatenated Coding System Block Diagram6.2 ENCODING AND DECODING A CONCATENATED CODEEncoding or decoding of a concatenated code is a simple matter of encoding or decoding thetwo codes in sequence.Interleaving between the Outer and Inner Codes — When concatenated coding is used. AViterbi decoder selects the most likely path through its trellis, based on the noisy receivedsymbols. This path sometimes diverges from and re-merges with the correct path, resultingin a burst of bit errors. Simulations show that the decoder sometimes follows the wrong pathfor as long as several constraint lengths (see figure 6-2), and that a little over half thedecoded bits are in error during those times. For the purpose of figure 6-2, the definition oferror burst is those bits generated while the decoder has diverged from the correct path. Itshould be noted that this is not a general definition of error burst or burst length, but it is thedefinition used for figure 6-2. This definition is equivalent to saying that for a (K,r)convolutional code, a burst begins and ends with bit errors, and cannot contain K-1 or moreconsecutive correct bits. The motivation behind this form of the definition of a burst as usedin figure 6-2 is that a string of K-1 consecutive correct bits will return the Viterbi decoder tothe correct decoding path.Without interleaving, Viterbi decoder burst error events would tend to occur within one RScodeword, so that one codeword would have to correct all of these errors. Thus there wouldbe a tendency for some codewords to have ‘too many’ errors to correct (i.e., greater than E).Note on Concatenated Codes - In the case of concatenated convolutional and RS codes, theencoding and decoding is done sequentially. It has been found that in some commercialdecoder equipment used for near-Earth missions, because of the way the nodesynchronization threshold is set in the convolutional (Viterbi) decoder (see 9.3.2) for anoutput BER of 1x10 -5 from that decoder, the Viterbi decoder cannot work, for a rate ½ code,below an E b /N o of about 4 dB. Hence the link designer must include an implementation lossCCSDS 130.1-G-2 Page 6-2 November 2012
Average Burst Length, bitsTM SYNCHRONIZATION AND CHANNEL CODING—SUMMARY OF CONCEPT AND RATIONALEfactor in the link budget to account for this. The net effect is that the output of the RSdecoder is almost error free.210110AVERAGE DENSIT Y OF ERRORS IN BURS T = 0.5 TO 0.6010-0.50.00.51.01.52.0 2.5 3.0E b/N o(dB)3.54.04.55.05.5Figure 6-2: Average Burst Length vs. SNR, at the Viterbi Decoder Output, K=7CCSDS Convolutional CodeTable 6-1 shows the frame lengths for all the recommended interleaving depths for the two(non-shortened) RS codes.Table 6-1: Frame Lengths for All Interleaving DepthsInterleaverFrame length L, bitsdepth I E=16 E=81 1784 19122 3568 38243 5352 57364 7136 76485 8920 95608 14272 15296CCSDS 130.1-G-2 Page 6-3 November 2012
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