Data compression for stream with small packet

[alpha_one_x86]

Hello, I search real time compression to compress my tcp stream. That's mean not wait more data to send compressed data.

On the view of client, the 50% (or more) of upload, will be of this kind:
Where the 4 first bytes is the packet/weft lenght: 00000007 400602
20% will be near: 0000000C c20003 4006024123

The upload will be near (50% of this query):
C00003
0100002152000000080074006f0074006f000200020200C8
02000021530206020801
0300002154
The rest is more than 200Bytes mainly (chat, file transfer, ...)

The chain is: raw data -> compression -> tcp socket -> decompression -> parsing, this chain will not need have delay (other than cpu + transmission speed).

What is the better algorithm in this case, to prevent overhead on small packet, and correction compression ratio on big packet? The speed not interest to me.
Thanks to your help.

[Bulat Ziganshin]

i don't understand color pictures, sample data stream of few megabytes would be much better