Motivated by recently derived fundamental limits on total (transmit +decoding) power for coded communication with VLSI decoders, this paperinvestigates the scaling behavior of the minimum total power needed tocommunicate over AWGN channels as the target bit-error-probability tends tozero. We focus on regular-LDPC codes and iterative message-passing decoders. Weanalyze scaling behavior under two VLSI complexity models of decoding. Onemodel abstracts power consumed in processing elements ("node model"), andanother abstracts power consumed in wires which connect the processing elements("wire model"). We prove that a coding strategy using regular-LDPC codes withGallager-B decoding achieves order-optimal scaling of total power under thenode model. However, we also prove that regular-LDPC codes and iterativemessage-passing decoders cannot meet existing fundamental limits on total powerunder the wire model. Further, if the transmit energy-per-bit is bounded, totalpower grows at a rate that is worse than uncoded transmission. Complementingour theoretical results, we develop detailed physical models of decodingimplementations using post-layout circuit simulations. Our theoretical andnumerical results show that approaching fundamental limits on total powerrequires increasing the complexity of both the code design and thecorresponding decoding algorithm as communication distance is increased orerror-probability is lowered.
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