What is the relationship between the code of an Area Control Center (US) and associated Flight Information Region? From the wiki page, what I understand is 


  an Area Control Center (ACC), also known as a Center (or in some cases, en-route, as opposed to TRACON control), is a facility responsible for controlling aircraft en route in a particular volume of airspace (a Flight Information Region). In the United States, such a Center is referred to as an Air Route Traffic Control Center (ARTCC).


My question: Is ARTCC code different from the ICAO-FIR code? Or are there anomalies?

For example, here's a NOTAM in the FAA site. AT the bottom, under the headline Other Information, the ARTCC code is given as ZDC. Can I safely assume that the ICAO-FIR code would be KZDC for that NOTAM?
KZDC is the FIR associated with the ZDC ARTCC.  Think of KZDC as the airspace itself (the flight information region), and ZDC as the facility which services it.