The Home Location Register (HLR) is a database of all the network's customers. Each sim card has an identity, which is associated with one or more phone numbers. The HLR stores this information, as well as where that sim is currently located, or at least which VLR it is currently in the care of.
There is normally more than one HLR on a network, but they work together as a sort of distributed database, rather than independently, and are split by phone number, not geographically.
The Number Portability Database (NPDB) holds information about the mobile phone numbers that were issued by a network, but are no longer on that network. If you want to switch to a different mobile network and take your number with you, you can. The range of numbers that you can switch between is called a "Portability Cluster". For any call to a number in that cluster, a lookup to the number portability database is required to find out which network the number is now on. Normally, this database is linked to the GMSC but how it is used varies from call type to call type, and from network to network.
The Visitor Location Register (VLR) keeps track of where all the mobiles roaming within its area are currently located. It is normal for a VLR to cover the same area as a Mobile Switching Centre (MSC), and they are usually built as one database, but this is not required.
The VLR also stores information about mobiles roaming to its area from other networks.
The Equipment Identity Register (EIR) keeps track of the hardware (the handset, as opposed to the sim card) being used. If a handset is reported lost or stolen, the EIR can record this and refuse calls through it if it is on a "black" list, or mark the calls for special attention if it is on a "grey" list.
At the instigation of the government, to reduce the numbers of mobile phones being stolen (or at least to make stolen phones less valuable) the mobile networks now share blacklists, so a handset reported stolen will be barred by all the UK networks.
The Authentication Centre (AUC) is part of the security system. It stores a copy of the private key for each sim card, so that when the network asks the sim card coded security questions, the AUC is able to say whether the coded replies are the right answers! There is more about all this in the security pages.
back to 'How Mobiles Work'