We consider wireless communication systems with compact planar arrays having densely spaced antenna elements in conjunction with one-bit analog-to-digital and digital-to-analog converters (ADCs/DACs). We provide closed-form expressions for the achievable rates with simple linear processing techniques for the uplink as well as the downlink scenarios while taking into account the effects of antenna mutual coupling. In the downlink case, we introduce the concept of non-radiating dithering to combat correlations of the quantization errors. Under higher antenna element density, we show that the performance of the quantized system can be made close to the ideal performance regardless of the operating signal-to-noise ratio.