We consider efficient communication over a B-block
Rayleigh-fading channel with a K-sparse N-length discrete-time 
impulse response (assuming 0<K<N<B), where the transmitter and
receiver do not know the channel's support nor its coefficients.
For this, we propose a belief-propagation based reception 
scheme to use in conjunction with a standard bit-interleaved coded 
OFDM transmitter.
Unlike conventional "decoupled" receivers, which use pilots 
to estimate the sparse channel and then use the subsequent channel
estimate for data decoding, ours performs sparse-channel estimation and 
data decoding jointly. 
Empirical evidence suggests that the proposed scheme yields performance
near genie-aided bounds and, in fact, achieves the channel capacity pre-log 
factor (1-K/B), while maintaining linear complexity in both the channel 
and block length.