1 g 1 page 3 2 june 2006 tm synchronization and

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ENCODER MODULATOR AND RF TURBO DECODER DEMODULATOR 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 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 [8]) 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 1/4 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...
View Full Document

This document was uploaded on 03/06/2014.

Ask a homework question - tutors are online