Introduction To Coding And Information Theory Steven Roman — Updated

By Steven Roman (Inspired by his lifelong work in mathematical literacy)

[ h(x) = -\log_2(p) ]

When your data corrupts, you are witnessing a violation of the Hamming distance. When your compression algorithm bloats instead of shrinks, you are witnessing low entropy. Introduction To Coding And Information Theory Steven Roman

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. By Steven Roman (Inspired by his lifelong work

In Shannon’s world,

Mathematically, the information content ( h(x) ) of an event ( x ) with probability ( p ) is: Introduction To Coding And Information Theory Steven Roman