Introduction to Digital Communication - Homework

This repository contains my homework submissions for the course "Introduction to Digital Communication".

Course Information

The course covered representation of digital modulation in time, vector and frequency domains, data transmission through AWGN channel, bandpass data transmission, equalization, optimum receiver design, carrier and pulse synchronization, error probabilities for binary/m-ary transmission, carrier modulation techniques, communications over fading multipath channels and an introduction to Information Theory and Coding.

Course Outline

The course covered the following topics over the semester:

1. Introduction to Digital Modulation
2. One and two dimensional digital modulation
3. Multidimensional and differential digital modulation
4. Power spectrum of digitally modulated signals
5. Band-pass/low-pass representation of digitally modulated signals
6. Band-pass/low-pass representation of random signals
7. Signal-space concepts for deterministic and random signals
8. Optimum receiver for digitally modulated signals under AWGN
9. Optimum demodulation and detection under AWGN II
10. Error analysis of digital modulation under AWGN
11. Synchronization
12. Digital transmission through band-limited channels
13. Signal design for band-limited channels
14. Channel equalization
15. Trellis representation for intersymbol interference
16. Maximum Likelihood Sequence Estimation-Viterbi Algorithm
17. Elements of Information theory: Information, entropy, mutual information
18. Source Coding Algorithms
19. Channel capacity and channel coding
20. Channel Coding

Repository Contents

This repository consists of:

• Homework problem statements and their corresponding solutions organized in separate folders:

  • Homework 0: This assignment focuses on problems related to Random Variables and Processes.
  • Homework 1: Modulate a given bit stream with various modulation schemes (BPSK, QPSK, 4-PAM, 16-QAM, Binary FSK). The output includes constellation diagrams, sinusoidal waveforms representing the symbols, and the modulated pulse stream.
  • Homework 2a & Homework 2b: These assignments involve evaluating the error rate for baseband systems.
  • Homework 3: This assignment focuses on phase and timing estimation in digital communication systems.
  • Homework 4: Design and performance evaluation of various types of equalizers, including Zero-Forcing Equalizers (ZFE), Minimum Mean Square Error (MMSE) equalizers, and Decision-Feedback Equalizers (DFE) under three different channel scenarios.
  • Homework 5: Implement and evaluate Viterbi and MMSE equalizers under different Inter-symbol Interference (ISI) channel scenarios.
  • Homework 6: This assignment focuses on various Information Theory topics, including entropy, conditional entropy, joint entropy, mutual information, prefix codes, Huffman codes, differential entropy, and channel capacity.

• Supporting MATLAB code and files used to solve the problems and generate the required diagrams, simulations, and calculations.

Note

These solutions are provided as a reference for similar problems and for personal review. Always adhere to your institution's academic integrity guidelines when using these materials.