AxC-CS: Approximate Computing for Hardware Efficient Compressed Sensing Encoder Design

Abstract

In this paper, we present an approximate computing framework for hardware-efficeint compressed sensing encoder design exploiting application-level error-resiliency, termed as AxC-CS (\underline {A}ppro\underline {x}imate \underline {C}omputing for \underline {C}ompressed \underline {S}ensing). We consider a 2-stage scalar quantization scheme during CS encoding process for physiological signals in sensor nodes and demonstrate numerically that bringing forward the quantization process to the input signals could lead to negligible difference in signal reconstruction as compared to the standard measurement quantization scheme, and a second stage quantization over the approximate measurement can be performed to restore the ratedistortion performance. The optimal quantization depth can be deterministic according to the adopted sensing matrices. For random binary sensing matrix adopted in this paper, [${\mathbf{log}}_{\mathbf{2}} (\mathbf{n}/2)/2$] bits quantization depth can be safely truncated without incuring noticable errors when $\ell_{1} -$minimization is used for signal recovery. Compared with standard CS with accurate operation, this leads to efficient CS encoder design with simultaneous area and power reduction, where 25% and 28% lower area and power consumption can be achieved on MIT-BIH Arrhythmia database, respectively.