A sparse-graph-coded filter bank approach to minimum-rate spectrum-blind sampling
Sampling of bandlimited signals whose frequency support is unknown is called spectrum-blind sampling. It has attracted considerable attention due to its potential for sampling much lower than the Nyquist rate. The minimum rate for spectrum-blind sampling has been established as twice the measure of the frequency support. We study this sampling problem and propose a novel sampling framework by leveraging tools from modern coding theory. Our approach is based on subsampling the outputs of a carefully designed sparse-graph-codedfilter bank. The key idea is to exploit, rather than avoid, the aliasing artifacts induced by subsampling, which introduces linear mixing of spectral components in the form of parity constraints for sparse-graph codes. Under the proposed sampling scheme, signal reconstruction becomes equivalent to the peeling decoding of sparse-graph codes in erasure channels. As a result, we can simultaneously approach the minimum sampling rate, while also having a computational cost that is linear in the number of samples. We support our theoretical findings through numerical experiments.