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We consider spectrally-efficient communication over a Rayleigh N-block-fadingchannel with a K- sparse L-length discrete-time impulse response (for 0<K<L<N),where neither the transmitter nor receiver know the channel's coefficients norits support. Since the high-SNR ergodic capacity of this channel has been shownto obey C(SNR) = (1-K/N)log2(SNR)+O(1), any pilot-aided scheme that sacrificesmore than K dimensions per fading block to pilots will be spectrallyinefficient. This causes concern about the conventional "compressed channelsensing" approach, which uses O(K polylog L) pilots. In this paper, wedemonstrate that practical spectrally-efficient communication is indeedpossible. For this, we propose a novel belief-propagation-based receptionscheme to use with a standard bit- interleaved coded orthogonal frequencydivision multiplexing (OFDM) transmitter. In particular, we leverage the"relaxed belief propagation" methodology, which allows us to perform jointsparse-channel estimation and data decoding with only O(LN) complexity.Empirical results show that our receiver achieves the desired capacity pre-logfactor of 1 - K/N and performs near genie-aided bounds at both low and highSNR.

Belief-propagation-based joint channel estimation and decoding for spectrally efficient communication over unknown sparse channels