Communication over Impulsive Noise Channels: Channel Coding vs. Compressed Sensing

In this paper, we study transmission over channels which suffer from additive white Gaussian noise and, simultaneously and independently, from impulsive noise. As classical channel coding is designed to deal with the first impairment and, as shown recently, compressed sensing (CS) is capable to deal with the latter disturbance, we compare both operations. In particular, the dualities between syndrome decoding and CS-based erasure decoding are enlightened and the underlying optimization criteria contrasted. We discuss options for the optimization of CS signal recovery w.r.t. tolerance to additional noise, and give first results on improving the immunity of channel decoding against impulsive noise. All theoretical derivations are supported by numerical examples.