Posted by: atri | August 29, 2007

## Lecture 2: Error Correction and Channel Noise

In today’s lecture, we defined what it means to correct errors. In turn that lead us to the question of how we model the channel noise. We also saw that the repetition code $C_{3,rep}$ can correct one error but cannot correct two errors (in the worst case noise model). We finished by briefly arguing that the parity code $C_{\oplus}$ cannot even correct one error.

Next class we are going to look a bit more into $C_{\oplus}$ (which among other things will motivate another basic parameter of a code) and introduce a more sophisticated code due to Hamming.

We will be using finite fields and vectors spaces in the next class or so. I will very briefly cover the basics but if you want to get a heads up, consult the very nice notes on algebra from Madhu Sudan’s course on coding theory.