Fundamentals of probability theory introduction for an undergraduate course in digital communications

Explores basic quantities related to events: sample space, event probability, Bayes' Theorem, Total Probability Theorem, Mutually Exclusive events, Independent Events, Bernoulli Trials, etc.

This problem demonstrates conditional probabilities through a simple computational example. The probability of drawing two specific cards from a deck of cards without replacement is computed.

This example defines and investigates a communication channel called the binary symmetric channel (BSC).

This example investigates repeat coding, an error control coding scheme that improves transmission reliability at the expense of reduced data rates.

Gives an overview of two important functions for describing random variables, the cumulative distribution function (CDF) and probability density function (PDF).

Examines the PDF and CDF of Gaussian random variables. Also, discusses other functions related to Gaussian random variables such as the Q function, error function, and complementary error function.

PDF and CDF concepts for a single random variable are extended to multiple random variables. This yields new quantities such as joint distributions, conditional distributions, and independent random variables.

Defines the mean, moment, variance, and central moment of a random variable. All of these quantities are computed using a weighted average of the random variable probability density function.

Examples performs several computations with a Gaussian random variable. Specifically, the Q-Function is used to compute the probability of the Gaussian random variable being less than or greater than a number.

This example investigates a continuous random variable X with associated probability density function p(x). The mean, mean-squared, and variance of the random variable are computed from the definition (i.e. taking the appropriate weighted average of the PDF).

Polar signaling uses a single pulse shape to transmit binary information (i.e. bits) by using positive/negative pulse amplitudes to convey bit information. The receiver can decode the original bit information by sampling the received pulse and decoding to a binary 0 or 1 depending on if the received sample value is negative or positive. This problem derives the density function of the received signal sample values in the presence of additive white Gaussian noise.