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Unformatted text preview: TIONAL
ENCODER * VITERBI
DECODER * MODULATOR
AND RF DEMODULATOR
AND RF INNER CODE *OPTIONAL: MAY BE BYPASSED Figure 3-1: Coding System Block Diagram: Concatenated Codes CCSDS 130.1-G-1 Page 3-2 June 2006 TM SYNCHRONIZATION AND CHANNEL CODING —SUMMARY OF CONCEPT AND RATIONALE TURBO
AND RF TURBO
AND RF Figure 3-2: Coding System Block Diagram: Turbo Codes
These codes are included in the CCSDS Recommended Standard because they provide
substantial coding gain over an uncoded system. They have already been incorporated, or are
planned to be incorporated, into nearly all missions of member agencies of the CCSDS.
3.4.1 CHANNEL CODING PERFORMANCE
MEASURES OF PERFORMANCE Performance of any channel code is measured by its error rate, relative to the amount of
resources required to make the channel good enough to achieve that error rate. This Green
Book shows the performance of the recommended codes on the additive white Gaussian
(AWGN) channel, for which the relevant measure of required channel resources is given by a
single parameter Eb/N0, the ratio of the received signal energy per information bit to the (onesided) spectral density of the white Gaussian noise. This channel parameter Eb/N0 is
commonly called the bit signal-to-noise ratio, or bit-SNR.
The error rates achieved by the recommended codes are measured and reported in this Green
Book in three different ways. The bit error rate (BER) measures the error rate for individual
bits; the word error rate (WER) measures the error rate for individual codewords; 2 and the
frame error rate (FER) measures the error rate for individual frames. These three error rates
are well correlated with each other for any given code, but one error rate cannot generally be
derived from another without an assumption of independence of errors. As an example, if a
frame comprises L independent bits, then FER = 1 – (1 – BER)L; this assumption is valid for
uncoded frames on the AWGN channel, but not for frames subjected to any of the nontrivial
recommended coding schemes.
2 There is a slight impreciseness in this definition of WER. The output of a decoder is generally an estimate of
the information bits that were encoded, not an estimate of the actual encoded codeword. Such a decoder makes
a ‘codeword error’ when at least one of its decoded information bits is incorrect. This interpretation is
consistent with the term ‘codeword error’ because re-encoding the information sequence will produce the
correct codeword if and only if the entire sequence of information bits is correct. CCSDS 130.1-G-1 Page 3-3 June 2006 TM SYNCHRONIZATION AND CHANNEL CODING —SUMMARY OF CONCEPT AND RATIONALE In some cases, some of these error rates are synonymous or uninformative. For example,
WER=BER for uncoded data because in this case each ‘codeword’ consists of one bit. Similarly,
FER=WER for CCSDS turbo codes, because in this case the CCSDS transfer frame consists of
the information bits from one turbo codeblock. A codeword for unterminated convolutional
codes is theoretically infinitely long, so WER=1 (except on an error-free channel) and thus WER
is not a very interesting measure of performance in this case. It is natural to define WER for
terminated convolutional codes. Even for unterminated convolutional codes it is valid to
compute FER on a segment (defining the frame) of the convolutional codeword.
3.4.2 FUNDAMENTAL LIMITS ON CODE PERFORMANCE Good channel codes lower the error rate in the data, or equivalently they can achieve desired
error rates more efficiently as a function of the bit-SNR Eb/N0 on the channel. Shannon (see
reference ) derived fundamental limits on the performance of all codes. There are coderate-dependent channel capacity limits on the minimum Eb/N0 required for reliable
communication that are theoretically achievable by codes of a given rate in the limit of
infinite block sizes. In addition, there are block-size-dependent limits that preclude capacityattaining performance when the code’s block size is also constrained.
Code-Rate-Dependent Capacity Limits — Figure 3-3 shows the Shannon-limit performance
curves for a binary-input additive white Gaussian noise (AWGN) channel for rates 1/6, 1/4, 1/3,
and 1/2. These curves show the lowest possible bit-energy-to-noise ratio Eb/N0 required to
achieve a given BER over the binary-input AWGN channel using codes of these rates.
10-1 RATE 1/2 10-2 RATE 1/3
RATE 1/6 BER 10-3 10-4 10-5 10-6
-1.5 -1.0 -0.5 0.0 0.5 Eb/No (dB) Figure 3-3: Capacity Limits on the BER Performance for Codes with Rates 1/2, 1/3,
1/4 and 1/6 Operating over a Binary Input AWGN Channel CCSDS 130.1-G-1 Page 3-4 June 2006 TM SYNCHRONIZATION AND CHANNEL CODING —SUMMARY OF CONCEPT AND RATIONALE For low BER, each of these capacity-limited performance curves approaches a vertical
asymptote dependent on the code rate. The asymptotes are at 1.1 dB for rate 2/3, 0.2 dB for
rate 1/2, -0.5 dB for rate 1/3, and -0.8 dB for rate 1/4. The vertical asymptote for the ulti...
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This document was uploaded on 03/06/2014.
- Spring '14