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Course Description


This is a graduate-level course in Digital Communication theory.  This course reviews basic concepts from random variables, random processes, and filtering of linear processes, and then spends a majority of the class analyzing different digital communication schemes.  These topics include line coding, baseband communication, binary communication, M-ary signaling, signal space concepts, maximum likelihood and minimax decision theory, symbol error and bit error performance analysis, matched filter derivation, coherent carrier modulation, noncoherent modulation, and intersymbol interference.  


The textbook used for the course is, "Introduction to Digital Communications", by M. Pursley.


The comprehensive set of videos listed below now cover all the topics in the course; 126 videos with 21+ hours of content.

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Video Lectures


  • Random Variable Review: (6 videos, ~56 minutes)

    • Topics include: Random variable definition, density and distribution functions, mean, variance, moments, correlated/uncorrelated random variables, independent random variables, Gaussian random variables

  • Random Process Review: (7 videos, ~75 minutes)

    • Topics include: Random process definition, density and distribution functions, mean function, autocorrelation function, stationary random processes, wide-sense stationary (WSS) random processes, cross-correlation and cross-covariance functions, Gaussian random process, white noise random process.

  • Random Processes in Linear Systems Review

    • Part 1 (5 videos, ~55 minutes): Linear systems​ review, random processes in stable systems, random process output example, mean function example and mean function output derivation

    • Part 2 (7 videos, ~54 minutes): Autocorrelation function output derivation, random process output power, discrete-time input/output relationship summary, Gaussian random process input/output relationship derivation

  • Frequency Domain Analysis of Random Processes (7 videos, ~52 minutes)

    • Topics Include: Power spectral density definition, properties, examples, White noise, PSD input/output relationship, PSD of amplitude modulated signals and random processes, band-pass frequency functions.​

  • Baseband Binary Communication

    • Part 1 (10 videos, ~117 minutes): Signal sets, transmitting binary data, linear receivers/filters, filter output, decision statics, and error probabilities

    • Part 2 (16 videos, ~163 minutes): Minimax decisions, Bayes decisions, matched filter derivation, matched filter properties, matched filter frequency-domain representation and correlation receiver representation, signal space and signal distance.

  • Coherent Communication

    • Part 1 (9 videos, ~111 minutes): Introduction to coherent communication, binary phase-shift keying (BPSK), amplitude-shift keying (ASK), M-ary amplitude-shift keying (M-ASK)

    • Part 2 (5 videos, ~58 minutes): Overview of minimax and Bayes M-ary decision rules, 4-ASK decision rules and performance, Gray coding bit assignments and error bounds.

    • Part 3 (9 videos, ~126 minutes): Introduction to 2-D modulation; M-QASK modulation, receiver analysis, maximum likelihood decisions, and symbol/bit error probabilities; M-QPSK modulation.

    • Part 4 (8 videos, ~81 minutes): Introduction to orthogonal modulation, orthogonal modulation receiver and bit assignments, M-ary frequency shift keying (MFSK), offset modulation, and bandwidth comparisons of 2-D modulation schemes.

  • Noncoherent Communication (12 videos, ~96 minutes)

    • Topics include: Motivation for noncoherent modulation, optimal receiver structure and largest statistic (LS) decision rule, probability of error derivation, and binary frequency-shift keying.​

  • Synchronization and Fading

    • Part 1 (5 Videos, ~44 Minutes)​: Example techniques for carrier synchronization, symbol synchronization, and frame synchronization; phase-lock loops (PLL), squaring loops, Costas loop, and early/late gate techniques.

    • Part 2 (4 Videos, ~53 Minutes): A two-ray model, Rayleigh fading, and performance analysis in the presence of Rayleigh fading.

  • Introduction to Information Theory and Error Control Coding

    • Part 1 (6 Videos, ~51 Minutes)​: Channel capacity and the channel error exponent, Shannon's capacity formula, block coding.

    • Part 2 (5 Videos, ~34 Minutes)​: Linear codes, generator matrices, parity-check matrices, syndrome decoding.

Practice Problems

File Downloads

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