turbo2 - Turbo Coding and MAP Decoding - Example 1...

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Turbo Coding and MAP Decoding - Example Copyright 2006 Charan Langton www.complextoreal.com 1 Intuitive Guide to Principles of Communications www.complextoreal.com Turbo decoding using the MAP algorithm Part 2 – A Step by step example k u s k p k y y , 1 , 1 s k p k y y , 2 , 2 EC2 EC1 Figure 1 – A rate 1/3 PCCC Turbo code In this example, we will use a rate 1/3 Turbo Code which has two identical convolutional codes. Note that since 2, s k y is a deterministically reshuffle version of 1, s k y , it is not transmitted. The second decoder is given s k y , and it then de-interleaves it to get its copy of 2, s k y which it needs for decoding. The coding trellis for each is given by the figure below. The blue lines show transitions in response to a 0 and red lines in response to a 1. The notation 1/11, the first number is the input bit, the next are two code bits. Of these, the first is what we called the systematic bit , and as you can see, it is same as the input bit. The second bit is the parity bit. Each code uses this trellis for encoding.
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Turbo Coding and MAP Decoding - Example Copyright 2006 Charan Langton www.complextoreal.com 2 00 10 0 1 s1 s3 s2 s4 s1 s3 s2 s4 Figure 2 – the trellis diagram of the rate 1/2 code RSC code For the example, we pick the information bit sequence: 1, 0, 1, 0, 1, 0, 0, which in bi-polar form is shown in Table 1. Code 1 encodes each of these bits as systematic and parity bits using the trellis in Fig. 7. The bits are coded in a bipolar format. Table 1 – Coded bits through first Encoder Code 1 k=1 k=2 k=3 k=4 k=5 k=6 k=7 Systematic 1 -1 1 -1 1 -1 -1 Parity bit, ENC1 1 1 -1 1 1 -1 -1 The sequence looks like this on the trellis diagram. k=1 k=2 k=3 k=4 k=5 k=0 k=6 k=7 s1 s3 s2 s4 Figure 3 – Trellis diagram for information (1, -1, 1, -1, 1, -1, -1) through first encoder The code 2 receives the same information bits but interleaved by a given pattern. Interleaving is an important issue in turbo coding. There are several different types of interleaving patterns other than the row column method you know. Here I have made up a “pseudo-random” interleaving pattern shown in Table 2. The deinterleaving pattern puts the bits back in the original order. Simulations shows that pseudorandom interleaving works best with turbo codes in AWGN channel. Table 2 – Interleaving patter from Encoder 1 to Encoder 2 and then deinterleaving back to Encoder 1 from Encoder 2 Interleaving 1-2 1-3 2-4 3-1 4-5 5-2 6-6 7-7 Deinterleaving 2-1 1-3 2-5 3-1 4-2 5-4 6-6 7-7
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Turbo Coding and MAP Decoding - Example Copyright 2006 Charan Langton www.complextoreal.com 3 After reordering the information sequence (1, -1, 1, -1, 1, -1, -1) into (1, 1, 1, -1, - 1, -1, -1) Encoder 2 codes the new sequence as in Table 3. Table 3 – Interleaved bits coded by Encoder 2 Code 2 k=1 k=2 k=3 k=4 k=5 k=6 k=7 Systematic 1 1 1 -1 -1 -1 -1 Parity bit, ENC2 1 -1 1 -1 -1 -1 -1 On the trellis diagram this new sequence is coded as shown in Figure 8.
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This note was uploaded on 02/07/2011 for the course EE 567 taught by Professor Tutorials during the Spring '11 term at Birla Institute of Technology & Science, Pilani - Hyderabad.

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turbo2 - Turbo Coding and MAP Decoding - Example 1...

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