Chatting in distributed quantization networks

Several key results in source coding offer the intuition that distributed encoding via vector-quantize-and-bin is only slightly suboptimal to joint encoding and oftentimes is just as good. However, when source acquisition requires the block length to be small, collaboration between sensors can greatly reduce distortion. For a distributed acquisition network where sensors are allowed to “chat” using a side channel, we provide exact characterization of distortion performance and quantizer design in the high-resolution (low-distortion) regime using a framework called distributed functional scalar quantization (DFSQ). The key result is that chatting can dramatically improve performance even when the intersensor communication is at very low rate. We also solve the rate allocation problem when communication links have heterogeneous costs and provide examples to demonstrate that this theory predicts performance at practical communication rates.