  We consider spectrally-efficient communication over a Rayleigh N-block-fading
channel 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 nor
its support. Since the high-SNR ergodic capacity of this channel has been shown
to obey C(SNR) = (1-K/N)log2(SNR)+O(1), any pilot-aided scheme that sacrifices
more than K dimensions per fading block to pilots will be spectrally
inefficient. This causes concern about the conventional "compressed channel
sensing" approach, which uses O(K polylog L) pilots. In this paper, we
demonstrate that practical spectrally-efficient communication is indeed
possible. For this, we propose a novel belief-propagation-based reception
scheme to use with a standard bit- interleaved coded orthogonal frequency
division multiplexing (OFDM) transmitter. In particular, we leverage the
"relaxed belief propagation" methodology, which allows us to perform joint
sparse-channel estimation and data decoding with only O(LN) complexity.
Empirical results show that our receiver achieves the desired capacity pre-log
factor of 1 - K/N and performs near genie-aided bounds at both low and high
SNR.
