The checksums don't match because in Perl you're computing the MD5 of the string in $filename (see the documentation for Digest::MD5).

I don't see that $checksum is set to a null value, as you say. It seems to me that it's set to "933be8d9a84230aa8162932102dd0bf0 compress_logs.pl\n". Maybe you want to chomp it before you use it?