UCLA Olga Radko Endowed Math Circle

10/23/2016 -- High School I: Exploring Error-Correcting Codes (Olga Radko)

We will discuss what we mean by information and what it means to transmit information. Of course, as you transmit information, errors can occur . Think of the children’s game “Broken Telephone”, where players take turns whispering a message made up by the first player to each other. The final message received by the last player could be very different from the original. While this is fun in a game, we usually try to avoid this as much as possible in real life. Can we create a code that has a built-in protection against transmission errors? What is the price that we have to pay for increasing accuracy? We will touch upon several ideas of Shannon’s Information Theory and work through several examples to find out.