Posted by: atri | April 6, 2011

## Lecture 30: Generalized Minimum Distance Decoding

In today’s lecture we saw all three versions of the GMD algorithm, which ultimately allowed us to show that we can have explicit codes on the Zyablov bound along with efficient decoding algorithms to correct up to half the Zyablov bound. This material is from Lecture 28 and 29 from Fall 2007.

In class, Eric asked about if we can avoid basically running the errors and erasures decoding algorithm. Here is one paper that does that. Here is another, somewhat more recent paper that has more general results (as well has relevant papers in its references). Finally, here is an even more recent paper.

I mis-spoke in class today. On Friday I’m going to show how one can explicitly achieve the capacity of $\mathrm{BSC}_p$ along with efficient decoding algorithms. We’ll talk about decoding of RS codes from next week.