Exploring Optimal Prefix Codes and Sampling Theory

Efficient Encoding and Sampling-Optimal Prefix Codes and Sampling Theory

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Description

A beginner's guide to Optimal Prefix Codes. This course should answer your basic questions about prefix codes. I am Suman Mathews, a math educator teaching mathematics for three decades.


Optimal Prefix Codes


A sequence consisting of only 0 and 1 is called a binary sequence. A binary sequence is used as a code for messages sent through certain channels. Now the question is, how do we decode the sequence correctly?


Given a binary sequence, a prefix code is a code, say, P, in which no sequence can be the prefix of any other sequence in that code. Prefix codes are represented by binary trees, as can be seen in the course.


We assign the symbol 0 to every edge that is directed towards the child in the left and the symbol 1 to every edge that is directed towards the child in the right. The concept of parent and child is explained during the course. My students just love it.


What is a weighted binary tree?


If we assign positive integers to the leaves of a binary tree, you get a weighted binary tree.  A tree which carries the minimum weight is called an optimal binary tree.


If we assign a prefix code for the symbols representing the leaves so that we get an optimal binary tree, that prefix code is called the optimal prefix code.  You'll learn a number of questions where you can construct an optimal prefix code for a string.


As a sequel to this course, you'll learn the sum and product rule. Note that sum stands for 'OR' and product stands for 'AND'.


Bonus-Understanding Sampling Theory. Learn how to calculate the expected mean and standard deviation and also learn how to use the Normal Distribution table.


I hope this course helps you! Share this with other students who may need this. Thank you!


What You Will Learn!

  • You will learn about Prefix Codes and Optimal Prefix Codes in Graph Theory
  • Optimal Prefix Code Calculator is illustrated- College Discrete Mathematics Students can use this.
  • You will learn how to create an Optimal Tree with minimum weight-College Discrete Mathematics with examples
  • Coding and Decoding is illustrated-Foundations for College Discrete Mathematics
  • You'll be introduced to the Sum and Product Rule in Combinatorics.
  • Learn the basics of Sampling Theory and how to use the Normal Distribution table

Who Should Attend!

  • This is a College Discrete Mathematics Course with examples. Optimal binary prefix codes for Engineering is discussed here.