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I Tlecture 13a

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A
Adithya Rao

The document discusses various ways that known error correcting codes can be modified, including puncturing, shortening, expurgating, extending, lengthening, and augmenting codes. It also covers interleaving, concatenated codes, and examples of convolutional codes. Modification methods allow creating codes of nearly any rate with slightly improved performance compared to the original code.

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Convolutional Codes Representation and Encoding ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
Modification to Known Codes ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
Modification to Known Codes… ,[object Object],[object Object],[object Object],[object Object],Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
Interleaving ,[object Object],[object Object],[object Object],[object Object],Depth Of Interleaving Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE 1 1 6 2 11 3 16 4 21 5  31 7  26 6 5 29 10 30 30 34 35 35 Length Order Bits Transmitted Order Bits Received
Concatenated Codes ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
Block Diagram of Concatenated Coding Systems Data Bits Outer Encoder Interleave Inner Encoder Modulator Channel De - Modulator Inner Decoder De- Interleave Outer Decoder Data Out Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
Practical Application : Coding for CD ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
Practical Application: Galileo Deep Space Probe ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
IS-95 CDMA ,[object Object],[object Object],Data Transmission in a 3 rd Generation PCS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
Example of Convolutional Code k=1, n=2, K=3 convolutional code Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
Example of Convolutional Code k=2, n=3, K=2 convolutional code Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
[object Object],[object Object],[object Object],[object Object],[object Object],Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
Example of Convolutional Code k=1, n=2, K=3 convolutional code Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
Example of Convolutional Code k=2, n=3, K=2 convolutional code Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
Example of State Diagram Representation Of Convolutional Codes k=1, n=2, K=3 convolutional code Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
Example of Trellis Diagram k=1, n=2, K=3 convolutional code Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
Encoding Example Using Trellis Representation k=1, n=2, K=3 convolutional code ,[object Object],[object Object],[object Object],Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
[object Object],[object Object],[object Object],[object Object],Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
Best Rate 1/2 Codes Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
Best Rate 1/3 Codes Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
Best Rate 2/3 Codes Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE

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I Tlecture 13a

  • 1.
  • 2.
  • 3.
  • 4.
  • 5.
  • 6. Block Diagram of Concatenated Coding Systems Data Bits Outer Encoder Interleave Inner Encoder Modulator Channel De - Modulator Inner Decoder De- Interleave Outer Decoder Data Out Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13. Example of Convolutional Code k=1, n=2, K=3 convolutional code Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
  • 14. Example of Convolutional Code k=2, n=3, K=2 convolutional code Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
  • 15.
  • 16.
  • 17. Example of Convolutional Code k=1, n=2, K=3 convolutional code Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
  • 18. Example of Convolutional Code k=2, n=3, K=2 convolutional code Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
  • 19.
  • 20. Example of State Diagram Representation Of Convolutional Codes k=1, n=2, K=3 convolutional code Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
  • 21.
  • 22. Example of Trellis Diagram k=1, n=2, K=3 convolutional code Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
  • 23.
  • 24.
  • 25.
  • 26. Best Rate 1/2 Codes Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
  • 27. Best Rate 1/3 Codes Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
  • 28. Best Rate 2/3 Codes Error Control Coding , © Brian D. Woerner , reproduced by: Erhan A. INCE
  • 29.