On the Total-Power Capacity of Regular-LDPC Codes with Iterative Message-Passing Decoders

TL;DR

This paper examines the minimum total power required for reliable communication over AWGN channels using regular-LDPC codes with iterative message-passing decoders, analyzing different VLSI complexity models and providing both theoretical and simulation-based insights.

Contribution

It proves order-optimal total power scaling under the node complexity model and highlights limitations under the wire model, offering new understanding of power efficiency in LDPC decoding.

Findings

Regular-LDPC with Gallager-B decoding achieves near-optimal power scaling under node model.

Regular-LDPC codes cannot meet fundamental power limits under wire model.

Total power increases significantly with communication distance and lower error probabilities.

Abstract

Motivated by recently derived fundamental limits on total (transmit + decoding) power for coded communication with VLSI decoders, this paper investigates the scaling behavior of the minimum total power needed to communicate over AWGN channels as the target bit-error-probability tends to zero. We focus on regular-LDPC codes and iterative message-passing decoders. We analyze scaling behavior under two VLSI complexity models of decoding. One model abstracts power consumed in processing elements ("node model"), and another abstracts power consumed in wires which connect the processing elements ("wire model"). We prove that a coding strategy using regular-LDPC codes with Gallager-B decoding achieves order-optimal scaling of total power under the node model. However, we also prove that regular-LDPC codes and iterative message-passing decoders cannot meet existing fundamental limits on total power under the wire model. Further, if the transmit energy-per-bit is bounded, total power grows at a rate that is worse than uncoded transmission. Complementing our theoretical results, we develop detailed physical models of decoding implementations using post-layout circuit simulations. Our theoretical and numerical results show that approaching fundamental limits on total power requires increasing the complexity of both the code design and the corresponding decoding algorithm as communication distance is increased or error-probability is lowered.