In Shannon’s world,
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. Introduction To Coding And Information Theory Steven Roman
If I tell you something you already know (e.g., "The sun will rise tomorrow"), I have transmitted very little information. If I tell you something shocking (e.g., "The sun did not rise today"), I have transmitted a massive amount of information. In Shannon’s world, If you receive a 7-bit
Think of entropy as the "randomness temperature." High entropy (like white noise or scrambled text) means high information density. Low entropy (like a repeating loop of silence or a predictable string of zeroes) means you can compress it down to almost nothing. Coding Theory: The Art of Reliable Imperfection If information theory is about efficiency , coding theory is about survival . If I tell you something you already know (e
[ H = -\sum_{i=1}^{n} p_i \log_2(p_i) ]