Internet-connected mobile processors used in cellphones, tablets, and internet-of-things (IoT) devices are generating and transmitting data at an ever-increasing rate. ese devices are already the most abundant types of processor parts produced and used today and are growing in ubiquity with the rapid proliferation of mobile and IoT technologies. Size and usage characteristics of these data-generating systems dictate that they will continue to be both bandwidth- and energy-constrained. e most popular mobile applications, dominating communication bandwidth utilization for the entire internet, are centered around transmission of image, video, and audio content. For such applications, where perfect data quality is not required, approximate computation has been explored to alleviate system bolenecks by exploiting implicit noise tolerance to trade o output quality for performance and energy benets. However, it is oen communication, not computation, that dominates performance and energy requirements in mobile systems. is is coupled with the increasing tendency to ooad computation to the cloud, making communication eciency, not computation eciency, the most critical parameter in mobile systems. Given this increasing need for communication eciency, data compression provides one eective means of reducing communication costs. In this paper, we explore approximate compression and communication to increase energy eciency and alleviate bandwidth limitations in communication-centric systems. We focus on application-specic approximate data compression, whereby a transmied data stream is approximated to improve compression rate and reduce data transmission cost. Whereas conventional lossy compression follows a one-size-ts-all mentality in selecting a compression technique, we show that higher compression rates can be achieved by understanding the characteristics of the input data stream and the application in which it is used. We introduce a suite of data stream approximations that enhance the compression rates of lossless compression algorithms by gracefully and eciently trading o output quality for increased compression rate. For dierent classes of images, we explain the interaction between compression rate, output quality, and complexity of approximation and establish comparisons with existing lossy compression algorithms. Our approximate compression techniques increase compression rate and reduce bandwidth utilization by up to 10× with respect to state-of-the-art lossy compression while achieving the same output quality and beer end-to-end communication performance.