Course Description

This course is the second of a two-term sequence. The focus is on coding techniques for approaching the Shannon limit of additive white Gaussian noise (AWGN) channels, their performance analysis, and design principles. After a review of Principles of Digital Communication I and the Shannon limit for AWGN channels, the course begins by discussing small signal constellations, performance analysis and coding gain, and hard-decision and soft-decision decoding. It continues with binary linear block codes, Reed-Muller codes, finite fields, Reed-Solomon and BCH codes, binary linear convolutional codes, and the Viterbi algorithm. More advanced topics include trellis representations of binary linear block codes and trellis-based decoding; codes on graphs; the sum-product and min-sum algorithms; the BCJR algorithm; turbo codes, LDPC codes and RA codes; and performance of LDPC codes with iterative decoding. Finally, the course addresses coding for the bandwidth-limited regime, including lattice codes, trellis-coded modulation, multilevel coding and shaping. If time permits, it covers equalization of linear Gaussian channels.

Lectures

• 

  1. Introduction to Principles of Digital Communication II

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  2. Performance of Small Signal Constellations

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  3. Hard-decision and Soft-decision Decoding, Part 1

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  4. Hard-decision and Soft-decision Decoding, Part 2

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  5. Introduction to Binary Block Codes, Part 1

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  6. Introduction to Binary Block Codes, Part 2

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  7. Introduction to Finite Fields, Part 1

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  8. Introduction to Finite Fields, Part 2

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  9. Introduction to Finite Fields, Part 3

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  10. Reed-Solomon Codes, Part 1

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  11. Reed-Solomon Codes, Part 2

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  12. Reed-Solomon Codes, Part 3

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  13. Introduction to Convolutional Codes, Part 1

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  14. Introduction to Convolutional Codes, Part 2

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  15. Introduction to Convolutional Codes, Part 3

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  16. Trellis Representations of Binary Linear Block Codes, Part 1

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  17. Trellis Representations of Binary Linear Block Codes, Part 2

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  18. Codes on Graphs, Part 1

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  19. Codes on Graphs, Part 2

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  20. The Sum-Product Algorithm, Part 1

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  21. The Sum-Product Algorithm, Part 2

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  22. Turbo, LDPC, and RA Codes, Part 1

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  23. Turbo, LDPC, and RA Codes, Part 2

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  24. Lattice and Trellis Codes, Part 1

  MIT
  Computer Science, Engineering (Electrical)
  David Forney
• 

  25. Lattice and Trellis Codes, Part 2

  MIT
  Computer Science, Engineering (Electrical)
  David Forney

Course Detail

Source:  MIT Open Courseware

License: 

Universities

• MIT

Subjects

• Computer Science
• Engineering (Electrical)

Educators

• David Forney

Related Resources

1. Syllabus [1] [1] http://ocw.mit.edu/OcwWeb/Electrical-Engineering-and-Computer-Science/6-451Spring-2005/Syllabus/index.htm
2. Course Calendar [1] [1] http://ocw.mit.edu/OcwWeb/Electrical-Engineering-and-Computer-Science/6-451Spring-2005/Calendar/index.htm
3. Course Reading [1] [1] http://ocw.mit.edu/OcwWeb/Electrical-Engineering-and-Computer-Science/6-451Spring-2005/Readings/index.htm
4. Midterm Exam 2002 [1] [1] http://ocw.mit.edu/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6-451Spring-2005/6E7EEBEE-CF1E-4095-A980-74C35F9C8C39/0/midterm02.pdf
5. Midterm Exam 2002 Solutions [1] [1] http://ocw.mit.edu/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6-451Spring-2005/E1C51847-7ACE-4F2C-8623-D0FAE4D6A903/0/midtermsol02.pdf
6. Final Exam 2002 [1] [1] http://ocw.mit.edu/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6-451Spring-2005/E4AEED49-5931-46BC-961E-EB35CB08E193/0/final02.pdf
7. Final Exam 2002 Solutions [1] [1] http://ocw.mit.edu/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6-451Spring-2005/8FC26938-7DF5-4685-95F1-EA5FC34B2F41/0/final02solns2.pdf
8. Midterm Exam 2003 [1] [1] http://ocw.mit.edu/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6-451Spring-2005/DD1B2151-1C38-4E4F-911D-F73C173CB66A/0/midterm03.pdf
9. Midterm Exam 2003 Solutions [1] [1] http://ocw.mit.edu/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6-451Spring-2005/63564142-CBF3-4208-B5F0-32C8C3C10252/0/midterm03solns.pdf
10. Final Exam 2003 [1] [1] http://ocw.mit.edu/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6-451Spring-2005/204FE753-872D-410F-9F37-D0958E177EF0/0/final03.pdf
11. Final Exam 2003 Solutions [1] [1] http://ocw.mit.edu/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6-451Spring-2005/6FF6BE3B-CB55-47FA-AC75-A9B4A576B14E/0/final03solns.pdf
12. Midterm Exam 2005 [1] [1] http://ocw.mit.edu/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6-451Spring-2005/1435F92E-3E8F-4877-892A-E18A7882828E/0/midterm005.pdf
13. Midterm Exam 2005 Solutions [1] [1] http://ocw.mit.edu/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6-451Spring-2005/30E258D0-AFAE-421A-A230-157998A8ABF5/0/midterm05solns.pdf
14. Final Exam 2005 [1] [1] http://ocw.mit.edu/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6-451Spring-2005/840A9CE2-F8D1-4DFE-9A6E-E0D37D8CFF80/0/final05.pdf
15. Final Exam 2005 Solutions [1] [1] http://ocw.mit.edu/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6-451Spring-2005/400F20BF-183E-4BB1-B3CB-714201B8FA32/0/final05solns.pdf