One way to reduce the noise in a video camera image is to reduce the cameras gain. One way to increase the brightness of the image is to add gain.
We all know that increasing the gain to lets say +6db will increase noise and generally the reverse holds true when you reduce the gain, the noise typically reduces and this may be helpful if you are going to do a lot of effects work, or just want a clean image.
However in most cases adding or removing gain reduces the cameras dynamic range as it will artificially clip or limit your low key or high key parts of the image. The maximum illumination level that a camera can capture is limited by the sensor or the gamma curves that the camera has. The black level or darkest part of the image is the point where the actual image signal compared to the sensor noise level is high enough to allow you to see some actual picture information (also known as noise floor). So the dynamic range of the camera is normally the range between the sensors noise floor and recording or sensor clipping point.
To maximise the cameras dynamic range the designers will have carefully set the nominal zero db gain point (native ISO) so that the noise floor is at or very close to black and the peak recording level is reached at the point where the sensor itself starts to clip.
The gain of the camera controls the video output and recording level, relative to the sensors signal level. If you use -3db gain you attenuate (reduce) the relative output signal. The highlight handling doesn’t change (governed by the sensor clipping or gamma curve mapping) but your entire image output level gets shifted down in brightness and as a result you will clip off or loose some of your shadow and dark information, so your overall dynamic range is also reduced as you can’t “see” so far into the shadows. Dynamic range is not just highlight handling, it is the entire range from dark to light. 3db is half a stop (6db = 1 stop) so -3db gain reduces the dynamic range by half a stop, reducing the cameras underexposure range without (in most cases) any change to the over exposure range, so overall the total dynamic range is reduced.
When you add gain the reverse happens. Generally how far the sensor can see into the shadows is limited by the sensors noise floor. Add 6db of gain and you will make the darkest parts of the image brighter by 6db, but you will also raise the noise level by the same amount. So while you do end up with brighter shadow details you can’t actually see any more picture information because the noise level has increased by the same amount. At the top end as the brightest sensor output is mapped to the maximum recording level at 0db, when you add gain this pushes the recording level beyond what can be recorded, so you loose 6db off the top end of your recordings because the recordings and output clips 6db earlier. So positive gain maintains the same shadow range but reduces the highlight recording range by 6db.
However you use it gain tends to reduce your dynamic range. Adding gain to cope with poor lighting tends to be the lesser of the two evils as generally if your struggling for light then overexposure and blown out highlights is often the last of your worries.
Negative gain is sometimes used in camera to try to reduce noise, but the reality is that you are loosing dynamic range. Really a better solution would be to expose just a tiny bit brighter and then bring your levels down a bit in post production.