Figure 6.1. A convolutional encoder

Figure 6.1. A convolutional encoder

Figure 6.2. Structure of a systematic convolutional encoder of rate

Figure 6.3. Convolutional encoder of rate

Figure 6.4. Encoder of convolutional code of code rate

Figure 6.5. State diagram for the convolutional encoder of Figure 6.3

Figure 6.6. Trellis representation of the convolutional code of Figure 6.3

Figure 6.7. A systematic convolutional encoder

Figure 6.8. A FIR FSSM

Figure 6.9. IIR FSSM

Figure 6.10. FIR FSSM in the discrete time domain

Figure 6.11. An IIR FSSM

Figure 6.12. Equivalent systematic convolutional encoder of the encoder of Figure 6.3

Figure 6.13. Trellis for the convolutional encoder of Figure 6.12

Figure 6.14. General structure of systematic IIR convolutional encoders of rate

Figure 6.15. Modified state diagram

Figure 6.16. Minimum free distance sequence evaluated on the trellis

Figure 6.17. Hamming distance calculations for the Viterbi algorithm

Figure 6.18. Survivor paths in the Viterbi algorithm

Figure 6.19. Viterbi decoding algorithm, time instant

Figure 6.20. Viterbi decoding algorithm, decoded sequence at time instant

Figure 6.21. Extended and modified state diagram

Figure 6.22. Vector representation (polar format) of code vectors in a vector space of dimension

Figure 6.23. Signal resulting from the transmission of the code vector in polar format over a Gaussian channel

Figure 6.24. A soft decision channel

Figure 6.25. A comparison between hard and soft decision decoding of the triple repetition code (n=3), and uncoded transmission

Figure 6.26. Hard decision decoding of example of Section 16.3

Figure 6.27. Trellis of the convolutional encoder of Figure 6.3 with output values in polar format

Figure 6.28. Soft decision decoding to determine the survivor at time instant on the corresponding trellis

Figure 6.31. Soft decision decoding to determine the final survivor on the corresponding trellis

Figure 6.32. Punctured convolutional encoder of rate based on a convolutional code of rate

Figure 6.33. Trellis for a punctured convolutional code of rate based on a convolutional code of rate

00/000 00/000 Sa=00 00/110 10/111 10/111 00/101 00/011 11/110 11/110 01/001 01/001 10/001 Sb=10 01/111 10/010 11/000 10/100 01/100 Sc=01 11/0110 01/010 Sd=11 11/101 Figure 6.34. Trellis for a convolutional code of rate constructed in the traditional way

Figure P.6.1. Convolutional encoder, Problem 6.3

Figure P.6.2. Convolutional encoder, problem 6.4

Figure P.6.5. Trellis diagram, problem 6.7

Figure 6.1. A convolutional encoder

Figure 6.1. A convolutional encoder

Presentation Transcript

Convolutional Codes

Figure 6.1 Philosophy and Professionalism

Convolutional codes

Figure 6.1

Convolutional encoding

Figure 6.1 Macroeconomics in Context

Encoder

Convolutional Networks

Figure 6.1. A 2-to-1 multiplexer.

Figure 6.1 A 2-to-1 multiplexer

Figure 6.1 Simplified service processes

Encoder

6. Appendix 6.1-6. Figures Figure 6.1

Figure 6.1 Histogram of temperature data.

Figure 6.1 Schematic view of query processing.

Convolutional Coding

Figure 6.1 Classification of epithelia.

Figure 6.1 Relationship between the main program and a procedure.

Figure 6.1 Stack of cafeteria dishes