"So you are looking for an 8051 version of Winzip?"

Actually, WinZip (and PKzip) uses a variety of compression techniques, depending on the nature of the data being compressed.

As Jez has already hinted, the type of algorithm most appropriate depends upon the nature of the data.

So it might be worth a read through the Winzip documentation, and their website - that should at least give you some terms to put into your favourite internet search engine!

Also try "V.42-bis" and "MNP 5"