Hard-decision and Soft-decision Decoding, Part 2

Lecture Description

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.

Related Resources

Lecture Notes   |  Problem set 3   |  Problem set 3 Solutions

Course Index

1. Introduction to Principles of Digital Communication II
2. Performance of Small Signal Constellations
3. Hard-decision and Soft-decision Decoding, Part 1
4. Hard-decision and Soft-decision Decoding, Part 2
5. Introduction to Binary Block Codes, Part 1
6. Introduction to Binary Block Codes, Part 2
7. Introduction to Finite Fields, Part 1
8. Introduction to Finite Fields, Part 2
9. Introduction to Finite Fields, Part 3
10. Reed-Solomon Codes, Part 1
11. Reed-Solomon Codes, Part 2
12. Reed-Solomon Codes, Part 3
13. Introduction to Convolutional Codes, Part 1
14. Introduction to Convolutional Codes, Part 2
15. Introduction to Convolutional Codes, Part 3
16. Trellis Representations of Binary Linear Block Codes, Part 1
17. Trellis Representations of Binary Linear Block Codes, Part 2
18. Codes on Graphs, Part 1
19. Codes on Graphs, Part 2
20. The Sum-Product Algorithm, Part 1
21. The Sum-Product Algorithm, Part 2
22. Turbo, LDPC, and RA Codes, Part 1
23. Turbo, LDPC, and RA Codes, Part 2
24. Lattice and Trellis Codes, Part 1
25. Lattice and Trellis Codes, Part 2