Well, noise is originating in the sensor, it's 'the dance of the molecules'.
But, compression can make its more obvious, DCT in particular, apart from cameras that do some filtering. Take Sony, for example, they do this in their hybrid cameras. Getting excellent low-light footage at the cost of loosing detail since that's no temporal filter.
Recently, Red started to use DCT too, while they were using Wavelet before. Wavelet is softening at higher compression, while DCT tends to produce blockiness. AFAIK, BM is also using DCT.