Chris Dorner vs. LAPD Update?

I know there were a lot of problems between Chris Dorner and LAPD, and I would like to have more updates about this. I heard only a few things about what happened, there are a lot of information but in the last updates they still don't know if Chris Dorner is dead or not. I heard that he was a LAPD officer and now he could face death penalty. I don't know exactly what happened but I would like to have more information about Chris Dorner vs. LAPD and the last updates.

The principal problem in all this situation was between Chris Dorner and LAPD, and the last update was yesterday when the LAPD Commander Andrew Smith said: "Enough is enough...it's time to stop the bloodshed."
This started when Chris Dorner posted a "manifesto" which explained why he is against the LAPD which fired him in 2008 and named a lot of people on a list beginning his revenge on February 3, 2013 by killing the daughter of a retired police captain and her fiancé.
All the time in the news they are updating information about Christopher Dorner and how the LAPD is acting. Although the last updates say that he is dead, we are not sure about this, but I'll be waiting for more news today, to finally know what happened.