The reed solomon rs code then encodes the symbols

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Unformatted text preview: ) uses either of the recommended RS codes (or shortened versions) together with any of the recommended convolutional codes (either of which may also be used separately under the Recommended Standard (reference [3])). A block diagram of this concatenated coding system is given in figure 6-1. The binary input data sequence is divided into 8-bit sequences to form symbols over a 28 = 256-ary alphabet. The Reed-Solomon (RS) code then encodes the symbols such that any combination of E or fewer symbol errors per RS word (255 symbols per word) can be corrected. The reason that the recommended concatenated code operates as an effective teaming of its outer and inner codes stems from the nature of Viterbi decoding. The decoded bit errors made by the constraint-length-7 convolutional decoder tend to clump together in reasonably short bursts. In a concatenated coding system that uses a convolutional inner code, the outer code should be tailored to the burst error environment created by the convolutional decoder. A (255,255–2E) Reed-Solomon outer code is a good match for the convolutional inner code with constraint length 7 because the bursts of errors from the convolutional decoder typically have burst lengths ranging from a few bits to several constraint lengths. This corresponds to only a small number of 8-bit symbols in the outer code, and hence only a moderate amount of interleaving is required to prevent a few long bursts from exceeding the error correction capability of the Reed-Solomon decoder. On the other hand, it is advantageous for Viterbi decoder errors to be clustered within individual RS symbols, because an RS symbol is equally wrong to the RS decoder whether it contains one bit error or eight bit errors. Because the Viterbi decoder errors occur in bursts comparable in length to the RS symbol size, 3 or 4 Viterbi decoder bit errors will typically be packed into a single RS symbol, and these cause much less damage than isolated bit errors to the error correction abilities of the outer code, at a given bit error rate of the inner code. In summary, the typical error bursts from a constraintlength-7 convolutional decoder are long enough to take advantage of packing Viterbidecoded bit errors into single 8-bit RS symbols, but not so long as to require an inordinate amount of interleaving to keep the Reed-Solomon code from being overwhelmed by overly lengthy error bursts. CCSDS 130.1-G-1 Page 6-1 June 2006 TM SYNCHRONIZATION AND CHANNEL CODING —SUMMARY OF CONCEPT AND RATIONALE FRAME SYNC PATTERN INSERTION DATA SOURCE REED-SOLOMON OUTER ENCODER SYMBOL INTERLEAVING BUFFER CONVOLUTIONAL INNER ENCODER MODULATOR NOISE CHANNEL DECODED DATA REED-SOLOMON DECODER FRAME SYNC AND SYMBOL DEINTERLEAVING VITERBI INNER DECODER DEMODULATOR Figure 6-1: Concatenated Coding System Block Diagram 6.2 ENCODING AND DECODING A CONCATENATED CODE Encoding or decoding of a concatenated code is a simple matter of encoding or decoding the two codes in sequence. Interleaving between the Outer and Inner Codes — When concatenated coding is used, interleaving is recommended because the inner Viterbi decoder errors tend to occur in bursts, which occasionally are as long as several constraint lengths (see figure 6-2). Without interleaving, Viterbi decoder burst error events would tend to occur within one RS codeword, so that one codeword would have to correct all of these errors. Thus there would be a tendency for some codewords to have ‘too many’ errors to correct (i.e., greater than E). CCSDS 130.1-G-1 Page 6-2 June 2006 TM SYNCHRONIZATION AND CHANNEL CODING —SUMMARY OF CONCEPT AND RATIONALE Average Burst Length, bits 10 10 2 1 AVERAGE DENSIT Y OF ERRORS IN BURS T = 0.5 TO 0.6 10 0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 E b /N o (dB) Figure 6-2: Average Burst Length vs. SNR, at the Viterbi Decoder Output, K=7 CCSDS Convolutional Code Table 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 Depths Interleaver Frame length L, bits depth I E=16 E=8 1 1784 1912 2 3568 3824 3 5352 5736 4 7136 7648 5 8920 9560 8 14272 15296 CCSDS 130.1-G-1 Page 6-3 June 2006 TM SYNCHRONIZATION AND CHANNEL CODING —SUMMARY OF CONCEPT AND RATIONALE 6.3 PERFORMANCE OF THE RECOMMENDED CONCATENATED CODING SYSTEMS Consider a concatenated coding system consisting of a (K,r) convolutional inner code of rate r and constraint length K, and an (n,k) Reed-Solomon outer code. It is assumed that the symbols are interleaved at a sufficient depth to insure that symbol errors are independent at the RS decoder input. Then the bit, symbol, and word error probabilities, Pb , Ps , and Pw , respectively, are given by the formulas in the previous section, in terms of Vs , the symbol error probability at the input of the RS decoder or equivalently at the output of the Viterbi decoder, and Vb, the bit error probability at the output of the Viterbi decoder. The ratio Vb / Vs is estimated empirically and depends on the burst statistics of the inner...
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This document was uploaded on 03/06/2014.

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