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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 ). 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 ) 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 ).
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.
- Spring '14