Fundamental limits and achievable strategies for low energy compressed sensing with applications in wireless communication

We consider energy-efficient decoding for multiuser detection in a wireless channel with n potential users, each of which participates with probability p. We model this problem as that of energy-efficient decoding for support recovery in a compressed sensing setup where the decoder is required to identify the support of the compressed signal vector. We use a communication complexity measure of “bit-meters” in our calculations because of its close connection to energy consumption. The measure focuses on energy required to move information on a computational substrate, which while a dominant cost in modern circuits, is not captured by the Turing machine model. In this model of energy consumption, we provide both upper bounds and lower bounds on required energy consumption in recovering the sensed signal. By comparing a lower bound on “fixed-schedule” decoding with an upper bound on “flexible-schedule,” we establish that allowing for flexibility in the schedule of message-passing at the decoder can reduce energy in order sense. This establishes the utility of adaptivity and asynchronicity in VLSI implementations of compressed sensing decoders and presents a contrast to prior works that show that both fixed schedule and flexible schedule architectures perform similarly in decoders for channel coding. Moreover, our decoder consumes (in an order-sense) fewer bit-meters than previous computationally efficient algorithms implemented directly on any flexible-scheduled decoders when the probability p is small enough.