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

The fundamental problem considered in this paper is “What is the $\mathit{\text{energy}}$ 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 $\mathit{\text{bit-meters}}$ 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 $\mathit{\text{bit-meters}}$ 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.