First Step is to build a Linux Transcoding Box
You can use almost any distribution that can run VLC and the HDHomeRun library, Popular distributions like Ubuntu and Debian should work. I have not tested it on Raspbian, but I think Raspberry Pi's CPU may not be enough to transcode, and right now I did not research how to use the Pi's GPU to transcode, I have a feeling if this can be figured out, that would be the ideal way to go. But the route I did decide to go with was a CentOS 6 64bit distro.
The hardware I am using will actually be a virtual machine on an ESXi server. It will be on a VM that has 2 cores which run on Xeon 2.26Ghz processors, 2GB of RAM, 20GB of hard drive space. The NIC I used was the VMXNET 3, but the switch that the HDHR connects to is 100MB, so I should be fine.
Build the linux box, no GUI needed
You will need to add a a third party repo to get VLC installed.
wget http://dl.atrpms.net/el6.9-x86_64/atrpms/stable/atrpms-repo-6-7.el6.x86_64.rpm
Then
yum install atrpms-repo-6-7.el6.x86_64.rpm
In the future, the above instructions may be obsolete, here is a link the their instructions
http://atrpms.net/documentation/install/
After that is installed, type
yum install vlc
To summarize, you need a box powerful enough to transcode with linux installed and VLC added on.
The version of vlc as of this writing that works with this document is
VLC media player 2.1.4 Rincewind