Can 4K video represent the same color information as 10bit HD?

So there was a debate over on provideocoallition.com –
 – on this subject and I thought I would chime in if someone is interested. And since I have a background in printing, I might be able to explain this in a slithtly different way than video-only people… perhaps?
So, here goes:
Yes, you can absolutely substitute bit depth for resolution – open any glossy print magazine and flip to a beautiful color ad, and you are looking at 1bit color – yes ONE-bit color. But with an extreme resolution. More on this below.

And yes, in theory 4K 8bit video can absolutely represent the same color information contained in HD 10bit video. But, the codec has to be geared towards this purpose.

Consider a 10bit HD pixel with a value of 1022 – this is just shy of the 1023 maximum value on the 0-1023 scale – a small, but important difference.
That same pixel in an 8bit system would be represented by a value of 255 – the Max value on the 0-255 scale. And, if this pixel were put into a 10bit container, the value would be 1023 – one off from the ”True” 10bit value.
However, suppose we upped the resolution of the 8bit system from HD to UHD. Now that single HD pixel is represented (spatially) by 4 8bit pixels. So in it’s simplest form – if the signal processing and codec is working at a higher bit depth right up until the actual ”number” encoding, it could encode the 4 pixels as 255, 255, 255, 254. So when the 4 UHD pixels are down sampled (averaged) into a 10bit HD pixel – it’s value would be the correct one: 1022.
However, if the signal processing/codec is not geared towards encoding the UHD this way – it’s all for nothing. If the codec simply encoded each UHD pixel as rounded to the closest 8bit value, you would end up with 255, 255, 255, 255 – and when this is downscaled into a 10bit container you end up with 1023 – not the ”true” 10bit value.
So, in summary, in theory FOUR UHD 8bit pixels (4 containers of 256 values) can hold the EXACT same amount of color information as ONE HD 10bit pixel (1 container of 1024 velues) – but everyhing in the signal processing/codec has to work towards this goal.
If this is true of real world camera/codec implementations or not, I’m not sure – this is another discussion, and I’m sure you can dig deep into this.
So, what about printing being a 1-bit color system…?!? Those glossy ads seem to have infinite color…
Have you ever been next to an offset priner?
It has 4 vats – one for black, one for yellow, one for cyan, and one for magenta. That’s IT – no shades or gradiations. And the colors are NOT ”mixed” per se to provide different shades (like you would see at Home Depot paint department where a machine will mix an exact amount of this, that and the other to provide any shade you want.)
No, Offset printing (the most common method for high quality printing) is a 1bit process, but working at an extreme resolution. To represent different shades of color, a RIP (Raster image processor) transforms a color image of any bit depth into a 1bit (per color channel) ”raster” that gets printed on the paper at a very high resolution. The raster can be either ”AM-modulated” where dots of varying sizes are printed on a fixed grid, or it can be ”FM-modulated” where a fixed size dot gets printed as varying intervals, or it can be a mix of the two methods (AM/FM-modulation).
But the point is: it’s a system where the RIP (which could be compared to the CODEC in video terms) substitutes Bit depth for resolution.
A color image that goes to print usually has a resolution of 300dpi color which gets ”RIPPED” into a 1bit raster at typically around 4.000 dpi.
So, to get back to the original question – can 4K 8bit video represent the same color information as HD 10bit – the answer is yes, if the codec and signal processing is geared towards this purpose.
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