Medium bit rate hybrid speech coding schemes have gained much interest in the recent years and many of them have been standardized for various applications. This work characterizes a speech codec in a Compressive Sensing (CS) framework. We mainly demonstrate two aspects 1) Simultaneous compression and de-noising of speech by CS 2) Appropriate quantization of CS measurements to design medium bit-rate codec. The proposed scheme renders better quality speech compared to CELP, the widely used hybrid coding scheme, at the same bit rates. The CS speech codec has the added advantage of inherent noise suppression and easy scalability, without complex parameter extractions and voice activity detections. © 2015 IEEE.