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

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June 2012
Publication year: 2012
Source:Physical Communication, Volume 5, Issue 2

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 the 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 ) log 2 ( 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 ( L N ) 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 .


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