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Advances of information-theoretic understanding of sparse sampling ofcontinuous uncoded signals at sampling rates exceeding the Landau rate werereported in recent works. This work examines sparse sampling of coded signalsat sub-Landau sampling rates. It is shown that with coded signals the Landaucondition may be relaxed and the sampling rate required for signalreconstruction and for support detection can be lower than the effectivebandwidth. Equivalently, the number of measurements in the corresponding sparsesensing problem can be smaller than the support size. Tight bounds oninformation rates and on signal and support detection performance are derivedfor the Gaussian sparsely sampled channel and for the frequency-sparse channelusing the context of state dependent channels. Support detection results areverified by a simulation. When the system is high-dimensional the required SNRis shown to be finite but high and rising with decreasing sampling rate, insome practical applications it can be lowered by reducing the a-prioryuncertainty about the support e.g. by concentrating the frequency support intoa finite number of subbands.

On sparse sensing and sparse sampling of coded signals at sub-Landau rates