Fixing the Broken Telephone

2017 edition

Ivan Bailera, Carlos Vela

The Chinese whispers, also known as the broken telephone, is an internationally popular game in which participants have fun listening how an initial message is distorted when transmitted along a chain of listeners. Errors typically accumulate in successive whispers, so the message announced by the last player significantly differs from the first one, usually with humorous effect.

In a communication scheme, as in the broken telephone game, there is a source (the first participant), a channel (the chain of listeners), a receiver (the last participant) and a message. The source send a message to the receiver over a channel. We say that a channel is noisy if the received message can be different from the sent message. Coding theory springs forth in order to study and solve this problem, detecting the errors and correcting them. Coding theory makes use of classical and modern algebraic techniques involving finite fields, group theory, and polynomial algebra. It has connections with other areas of discrete mathematics, especially number theory and the theory of experimental designs.

The aim of this talk is to introduce the mathematics of error-correcting codes using the broken telephone game.