Random demodulator in matrix form I went through a paper in random demodulator. It states that If the sampling rate is $R$ ($R$ is less then $W$, $W=$band limit of a signal in Hz), and assume that $W$ is divided by $R$. Then each sample is the sum of $W/R$ consecutive entries of the demodulated signal. Does it mean that the signal is compressed by taking $W/R$ samples at a time?
The random demodulator (in this definition) compresses the signal by taking samples that are each linear combinations of W/R Nyquist rate samples. So it does not take W/R samples at a time; it takes one sample at a time, each of which contain information corresponding to several (W/R) Nyquist rate samples. It is then up to a reconstruction algorithm to subsequently "disentangle" these into the original signal (approximately) at Nyquist rate.

The random demodulator works by "smearing" the content of the input signal all over the spectrum (by multiplication with the spreading sequence). Provided that the input signal is sufficiently sparse, we can now reconstruct it from just a small portion of the resulting spectrum (selected by the low-pass filter).