The Radeon HDMI audio support within the open-source AMD Linux graphics driver has traditionally lagged behind other parts of the Radeon driver and hasn't been as great as some other audio adapters in terms of features and support. The original Radeon HDMI audio support was done through reverse-engineering as AMD hadn't revealed any audio specifications or documentation. The community beat AMD in this regard.
Basic Radeon HDMI audio support was only merged in Linux 2.6.33 and it ended up being disabled by default over issues affecting some users. Right now the Radeon HDMI audio support is still off-by-default but that might change soon now that the HDMI audio code mimics more closely the AMD Catalyst driver.
The situation improved in late September when AMD finally released Radeon audio documentation as well as expanding the documentation one week later.
For a few days now Anssi Hannula has been floating new ALSA HDA patches that improve the AMD Radeon hardware support. The set of four patches provide HBR bit-streaming support, more complete ELD (EDID-like data for audio) emulation, and some other changes. The big work is the multi-channel support and HBR bit-streaming.
The patched driver can now handle HD pass-through for DTS-HD and Dolby TrueHD audio on AMD Radeon hardware after NVIDIA and Intel have already supported this audio capability on Linux. The apparent issue in part has been that AMD HDMI codecs don't implement the standard support but rather are using custom verbs for the various elements. HBR allows up to eight audio channels compared to the Radeon driver previously just handling two channels.
So far the results I've heard from individuals testing these HDA HDMI audio patches for the Linux kernel have been positive. The patches amount to over 500 lines of new code for the HDA sound driver. Let's hope the continued testing continues to be joyful and that this work can land into the Linux 3.13 kernel. Those wanting to help test out the current kernel sound patches can find them on the ALSA-devel mailing list.