Principles of Digital Communication II

This course is the second of a two-term sequence with 6.450. 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 6.450 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.

• chap_1.pdf
• chap1_3.pdf
• Lecture 1: Introduction Sampling Theorem
• chap_2.pdf
• Lecture 2: Performance of Small Signal Constellations
• chap_3.pdf
• Lecture 3: Hard-decision and Soft-decision Decoding
• chap4.pdf
• Lecture 4: Hard-decision and Soft-decision Decoding
• chap_5.pdf
• Lecture 5: Introduction to Binary Block Codes
• chap6.pdf
• Lecture 6: Introduction to Binary Block Codes
• chap7.pdf
• Lecture 7: Introduction to Finite Fields
• chap8.pdf
• Lecture 8: Introduction to Finite Fields
• chap9.pdf
• Lecture 9: Introduction to Finite Fields
• chap10.pdf
• Lecture 10: Reed-Solomon Codes
• chap11.pdf
• Lecture 11: Reed-Solomon Codes
• chap12.pdf
• Lecture 12: Reed-Solomon Codes
• chap13.pdf
• Lecture 13: Introduction to Convolutional Codes
• chap14.pdf
• Lecture 14: Introduction to Convolutional Codes
• Lecture 15: Trellis Representations of Binary Linear Block Codes
• Lecture 16: Trellis Representations of Binary Linear Block Codes
• Lecture 17: Codes on Graphs
• Lecture 18: Codes on Graphs
• Lecture 19: The Sum-Product Algorithm
• Lecture 20: Turbo, LDPC, and RA Codes
• Lecture 21: Turbo, LDPC, and RA Codes
• Lecture 22: Lattice and Trellis Codes
• Lecture 23: Lattice and Trellis Codes
• Lecture 24: Linear Gaussian Channels
• Lecture 25: Linear Gaussian Channels