I am running 2 HDMI inputs into my Samsung 4k KU6300 50 inch tv, an HD Cisco cable box from Time Warner, and a Roku 3. I spoke to Samsung and they told me that the optical digital output of the tv DOES PASS 5.1 surround through the optical output on the tv, but I'm not 100% convinced the person on the end of the Samsung phone knew what he was talking about. I have to convert the optical audio out on the tv to coax. The coax digital audio is then run into the coax audio input of a Denon 3803 Denon receiver that has no HDMI inputs. I have the Denon receiver surround mode set to "AUTO". When I select HDMI 1 on the tv which is the Cisco HD cable box from Time Warner, on certain channels I select on the cable box the receiver readout on the front of the receiver displays "Dolby Digital" as the mode the receiver is in (a mode selected automatically by the receiver).
Question one is... Am I correct in saying because the receiver display reads "Dolby Digital" on certain selected channels this is telling me that the optical out of the tv is really passing/putting out full 5.1 Dolby Digital Surround Sound? Am I also correct in saying the toslink to spdif converter I am using is not causing a problem with outputting Dolby Digital?

Question 2 is... Why then when I select the HDMI 2 input on the tv which is the Roku 3, and I play the movie Inferno from Amazon which displays the logo "5.1", why does the receiver set the surround mode to NEO 6, and not Dolby Digital? I thought a movie on Amazon that displays the logo 5.1 is in true Dolby Digital. In fact when I manual set the receiver mode to Dolby Digital while the movie is playing I get no audio whatsoever. What is going on here? Any thoughts.

Question 3... Isn't Neo 6 a format that makes 2 channels of audio into a simulated surround sound kind of like the old Dolby Pro Logic did?
Thanks for the help.

DD is a digital signal, but that can mean 2.0 (stereo) all the way up to 5.1

You have to make sure that the Roku settings are correct for DD.
"Audio Mode (Auto (Dolby D+, DTS))"
"HDMI (Dolby D+, DTS)"

You also want to make sure you audio settings in cablebox are correct as well.

I already answered this is your other thread.
1) Yes, the cable box is outputting Dolby Digital 5.1. So your TV can take that signal and output it on the optical output to your Denon.
2) The Roku3 does "NOT" output DD from streaming streaming services like Netflix, Vudu, Amazon, etc... That is because the Roku3 does not convert DD+ to DD. And all those streaming services are using DD+. So the TV is getting DD+ (which is an HDMI only format) and the TV will not convert it either. So the TV is sending the only audio from that stream it can decode and that's 2ch PCM.

As before: you need to either get a new receiver with HDMI. Or a Roku Ultra that has the optical output built in, with regular DD5.1 output.

Your TV does provide 5.1 passthrough for DD signals [Link: rtings.com]
You are correct neo:6 is a " fake " surround, which basically means that your receiver is using buit-in decoder to convert two channel into multi-channel audio
[Link: lifewire.com]