web socket decompressing issue

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Hello, I'm building my own packet capture program using libpcap with c++. I wanted to capture a web socket protocol. I faced a problem while captureing it. I am using stomp library, and using permessage-deflate.

I looked at structure of web socket protocol. I successfully unmasked payload data using mask key. It looked just the same as wireshark's unmasked data. But the problem is here.

I heard that web socket protocol uses deflate compression to compress data. So I tried to decompress data which I already have unmasked. I used zlib that chatGPT gave me. But It kept saying error -3: data error. It says that data I tried to decompress is not a compressed data.

I also tried to compress data using zlib, but the result was different from wireshark's compressed data.

I want to know how wireshark successfully decompress data using deflate algorithm. I also want to know how to code it.

plz help me this is killing me for days..

below is hex stream data Decompressed payload(115bytes) : 53454e440a64657374696e6174696f6e3a2f7075622f636861740a636f6e74656e742d6c656e6774683a36380a0a7b2273656e646572223a22686874626f79222c20226368616e6e656c4964223a3630302c202263686174223a2268656c6c6f222c202274696d65223a2231303a3030227d00

Unmasked data(88bytes) : 0a76f5734155500055c0959c9f57929a57a29b939a975e92616566c1c555ad549c9a97925aa464a594915192945fa9a4a3a004549c97979ae399a204720544a004a4223527271fa4a024333715c83734b0323050aa650000