Steven Roman | Introduction To Coding And Information Theory

If you receive a 7-bit string, you run the parity checks. The result (called the syndrome) is a binary number from 001 to 111. That number tells you exactly which bit to flip to fix the message.

In Shannon’s world,

Entropy is the average amount of information produced by a source. It is also the minimum number of bits required, on average, to encode the source without losing any information. Introduction To Coding And Information Theory Steven Roman

By Steven Roman (Inspired by his lifelong work in mathematical literacy) If you receive a 7-bit string, you run the parity checks

Mathematically, the information content ( h(x) ) of an event ( x ) with probability ( p ) is: In Shannon’s world, Entropy is the average amount

This is not a tutorial on Python. This is an exploration of the mathematical bones of the digital age. Before Claude Shannon, the father of information theory, information was a philosophical or semantic concept. Shannon did something radical: he stripped meaning away entirely.

[ H = -\sum_{i=1}^{n} p_i \log_2(p_i) ]