Re: gsm
It stands for :
Regular Pulse Excitaion - Linear Predition Code
LPC is based on slow changing signals like voice , over a short window of samples can be used to expect the next sample with certain degree of error that can be minimized by acurate statistics , the idea is instead of sending the voice samples , we will send a filter parameters that can tun a generator to generate a voice-like signal that is very close to the original speech , this filter (voice generator) needs an excitation signal to start tuning and producing voice signals , and there are many excitaion methods
if you want to know more specific data on this topic i suggest you the book titled :
Digital Speech - coding for low bit rate communication systems
By: A. M. Kondoz