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

Abstract: 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.