We had already posted how this functionality will work from within CRM. Please follow the link below to refer the post.
Now it’s also possible to have this functionality in CRM Self Service web site. Self service users that are assigned the rights to access Self service website from CRM can login to the website and log the cases. We can also have communications functionality as that of the CRM in Self Service in order to maintain communications against particular case. These communications can be maintained in the threaded view as we can see on most of the blogs and forum sites. Due to threaded structure of communications we can have a clear idea of the communications that took place till date for that particular topic of interest by only looking at it once. Please refer below screenshot to get the clear picture of the functionality.