mu and alpha law encoding (u-law and a-law)are simple ways to mildly reduce the amount of bits needed per sample. Used in telephony. Look for "G.711". Basically, it serves to extend the dynamic range you would ordinarily be able to achieve with a certain amount of bits, by using a non-linear lookup table.
More effective datacompression can be achieved through ADPCM (Adaptive Differential Pulse Code Modulation), which has a low coding delay. Look for "G.721" and "G.722". It transmits the error signal between the original and a predicted signal at the transmitter end, and uses the error signal to correct the output of a similar predictor at the receiver end. An interesting variety of ADPCM is APTX, which is an optimised, multiband version of ADPCM.
The highest degree of data compression is achieved with CELP, as used in GSM phones. This type of compression is very destructive to the original signal, and because of the heavy calculations involved, it has some coding delay.
You will undoubtedly be familiar with "MP3", which I would not recommend for compression of a voice signal. It's destructive to the original signal, has a very long coding delay, and was not aimed at voice communications. If you don't mind the delay, MP3 is still interesting though.

Any method besides the mild u-law and a-law will require more processing power than an 8051 will offer you, and will either require an 8051 with onboard hardware codecs, or a DSP. Generally, I'd recommend ADPCM.

A link:

http://www-mobile.ecs.soton.ac.uk/speech_co...standards/