Posted by: atri | April 7, 2009

## Lecture 31: Minimum Distance Decoding

In Monday’s lecture, we saw the intuition and the statement of the (first randomized version of) GMD algorithm. Unfortunately, we ran out of time while proving that in expectation, the algorithm works. In particular, we were proving the following: for every $1\le i\le N$,

$\mathbb{E}[2X_i^e+X_i^?]< \frac{2e_i}{d}$.

Please read up on the algorithm and the part of the proof we did today for Wednesday’s lecture as we will start from where we left off today. To jog your memory, the stuff that we covered today is from the scribed notes of Lecture 28 from fall 07. (The proof will be a case analysis and hence a bit dry and I do not want to spend much time on it.)