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Figure 6.1. A convolutional encoder
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Figure 6.2. Structure of a systematic convolutional encoder of rate
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Figure 6.3. Convolutional encoder of rate
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Figure 6.4. Encoder of convolutional code of code rate
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Figure 6.5. State diagram for the convolutional encoder of Figure 6.3
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Figure 6.6. Trellis representation of the convolutional code of Figure 6.3
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Figure 6.7. A systematic convolutional encoder
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Figure 6.8. A FIR FSSM
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Figure 6.9. IIR FSSM
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Figure 6.10. FIR FSSM in the discrete time domain
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Figure 6.11. An IIR FSSM
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Figure 6.12. Equivalent systematic convolutional encoder of the encoder of Figure 6.3
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Figure 6.13. Trellis for the convolutional encoder of Figure 6.12
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Figure 6.14. General structure of systematic IIR convolutional encoders of rate
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Figure 6.15. Modified state diagram
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Figure 6.16. Minimum free distance sequence evaluated on the trellis
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Figure 6.17. Hamming distance calculations for the Viterbi algorithm
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Figure 6.18. Survivor paths in the Viterbi algorithm
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Figure 6.19. Viterbi decoding algorithm, time instant
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Figure 6.20. Viterbi decoding algorithm, decoded sequence at time instant
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Figure 6.21. Extended and modified state diagram
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Figure 6.22. Vector representation (polar format) of code vectors in a vector space of dimension
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Figure 6.23. Signal resulting from the transmission of the code vector in polar format over a Gaussian channel
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Figure 6.24. A soft decision channel
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Figure 6.25. A comparison between hard and soft decision decoding of the triple repetition code (n=3), and uncoded transmission
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Figure 6.26. Hard decision decoding of example of Section 16.3
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Figure 6.27. Trellis of the convolutional encoder of Figure 6.3 with output values in polar format
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Figure 6.28. Soft decision decoding to determine the survivor at time instant on the corresponding trellis
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Figure 6.29. Soft decision decoding to determine the survivor at time instant on the corresponding trellis
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Figure 6.30. Soft decision decoding to determine the survivor at time instant on the corresponding trellis
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Figure 6.31. Soft decision decoding to determine the final survivor on the corresponding trellis
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Figure 6.32. Punctured convolutional encoder of rate based on a convolutional code of rate
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Figure 6.33. Trellis for a punctured convolutional code of rate based on a convolutional code of rate
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Figure 6.34. Trellis for a convolutional code of rate constructed in the traditional way 11/110 00/000 01/001 10/111 11/101 01/010 10/100 11/011 0 01/100 10/010 11/000 01/111 10/001 00/011 00/101 00/110 11/110 00/000 01/001 10/111 S a =00 S b =10 S c =01 S d =11
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Figure P.6.1. Convolutional encoder, Problem 6.3
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Figure P.6.2. Convolutional encoder, problem 6.4
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Figure P.6.3. Convolutional encoder, Problem 6.5
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Figure P.6.4. Convolutional encoder, Problem 6.6
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Figure P.6.5. Trellis diagram, problem 6.7
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Figure P.6.6. Convolutional encoder, Problem 6.8
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