In principle any frame length l up to 16384 bits

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Unformatted text preview: —SUMMARY OF CONCEPT AND RATIONALE Figure 4-6: Bit Error Rate Performance of the CCSDS Rate-1/2 Convolutional Code with Different Decoding Delays D Telemetry data are collected in packets and transmitted in frames (see reference [2]). In principle, any frame length L up to 16384 bits could be acceptable. In figure 4-7 the Frame Error Rate (FER) at the output of the Viterbi decoder is reported for different frame lengths corresponding to those used for the concatenated (Reed-Solomon (255,223) + convolutional code) CCSDS code. A frame is in error if any of its constituent bits is in error. These curves have been obtained with unquantized soft decision and decoding delay D = 60 bits. Since the Viterbi decoder’s errors occur in bursts, the FER curves in figure 4-7 cannot be directly derived from the BER curve for D = 60 bits in figure 4-6 by assuming independent bit errors. Figure 4-7: Frame Error Rate Performance of the CCSDS Rate-1/2 Convolutional Code with Different Frame Lengths and Decoding Delay D=60 CCSDS 130.1-G-1 Page 4-8 June 2006 TM SYNCHRONIZATION AND CHANNEL CODING —SUMMARY OF CONCEPT AND RATIONALE 4.6 PERFORMANCE OF THE RECOMMENDED PUNCTURED CONVOLUTIONAL CODES The bit error rate performance of the CCSDS punctured convolutional codes is reported in figure 4-8. The curve relative to the non-punctured rate-1/2 CCSDS code is also reported for the sake of comparison. The expected performance degradation is confirmed (there is a gap of about 2.4 dB between the case of rate 1/2 and the case of rate 7/8), due to reduced bandwidth expansion. (All the curves have been obtained with unquantized soft decision and decoding delay equal to 60 bits.) The frame error rate performance of the CCSDS punctured convolutional codes is reported in figure 4-9 for frame size 8920 bits. NOTE – The performance of the original rate 1/2 code is reported for comparison. Figure 4-8: Bit Error Rate Performance of the CCSDS Punctured Convolutional Codes CCSDS 130.1-G-1 Page 4-9 June 2006 TM SYNCHRONIZATION AND CHANNEL CODING —SUMMARY OF CONCEPT AND RATIONALE NOTE – The performance of the original rate 1/2 code is reported for comparison. Figure 4-9: Frame Error Rate Performance of the CCSDS Punctured Convolutional Codes with Frame Length L=8920 CCSDS 130.1-G-1 Page 4-10 June 2006 TM SYNCHRONIZATION AND CHANNEL CODING —SUMMARY OF CONCEPT AND RATIONALE 5 5.1 REED-SOLOMON CODE INTRODUCTION Reed-Solomon (RS) codes (see reference [22]) are a particularly interesting and useful class of linear block codes. The block length n of an RS code is q–1, with q = 2J being the alphabet size of the symbols. RS codes with k information symbols and block length n have a minimum distance d = n–k+1. These codes have been used effectively in a concatenated code scheme (see section 6), where the symbols in an ‘outer’ RS code are further encoded by an ‘inner’ convolutional code. The error probability is an exponentially decreasing function of the block length, and the decoding complexity is proportional to a small power of n–k. ReedSolomon codes can be used directly on a channel with a small input alphabet by representing each letter in a codeword by a sequence of channel letters. Such a technique is useful on channels where the errors are clustered, since the decoder operation depends only on the number of sequences of channel outputs that contain errors. Using symbols with q = 2J for some J, the block length is n = 2J–1. For an arbitrarily chosen odd minimum distance d, the number of information symbols is k = n–d+1 and any combination of E = (d–1)/2 = (n–k)/2 errors can be corrected. If we represent each letter in a codeword by J binary digits, then we can obtain a binary code with kJ information bits and block length nJ bits. Any noise sequence that alters at most E of these n binary J-tuples can be corrected, and thus the code can correct all bursts of length J(E–1)+1 or less, and many combinations of multiple shorter bursts. Therefore RS codes are very appropriate on burst noisy channels such as a channel consisting of a convolutional encoder-AWGN channelViterbi decoder. RS codes are less appropriate for direct application to the AWGN channel where their performance is poorer than that of convolutional codes (see figure 3-5). The Reed-Solomon code, like the convolutional code, is a transparent code. This means that if the channel symbols have been inverted somewhere along the line, the decoders will still operate. The result will be the complement of the original data (except, usually, for the codeblock in which the inversion occurs). However, the Reed-Solomon code loses its transparency if virtual zero fill is used. For this reason it is mandatory that the sense of the data (i.e., true or complemented) be resolved before Reed-Solomon decoding, as specified in the Recommended Standard (reference [3]). Two RS codes are recommended by CCSDS, both having codeblock size n = 255 symbols and symbol size J = 8 bits or alphabet size 2J = 256. The first code has information block size k = 223, m...
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This document was uploaded on 03/06/2014.

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