Energy-efficient Decoders for Compressive Sensing: Fundamental Limits and Implementations

TL;DR

This paper establishes fundamental energy consumption limits for compressive sensing decoders using the information-friction framework and demonstrates that certain implementations approach these limits, guiding energy-efficient circuit design.

Contribution

It derives a fundamental lower bound on energy (bit-meters) for compressive sensing decoding circuits and shows existing algorithms are asymptotically optimal in energy efficiency.

Findings

Bit-meters consumption matches the lower bound asymptotically.

Energy-efficient circuit designs can approach fundamental energy limits.

Insights into circuit design beyond computational efficiency.

Abstract

The fundamental problem considered in this paper is "What is the \textit{energy} consumed for the implementation of a \emph{compressive sensing} decoding algorithm on a circuit?". Using the "information-friction" framework, we examine the smallest amount of \textit{bit-meters} as a measure for the energy consumed by a circuit. We derive a fundamental lower bound for the implementation of compressive sensing decoding algorithms on a circuit. In the setting where the number of measurements scales linearly with the sparsity and the sparsity is sub-linear with the length of the signal, we show that the \textit{bit-meters} consumption for these algorithms is order-tight, i.e., it matches the lower bound asymptotically up to a constant factor. Our implementations yield interesting insights into design of energy-efficient circuits that are not captured by the notion of computational efficiency alone.