On source-channel coding over Gaussian sensor networks for path planning

Path planning is an important component of mobile sensor and autonomous mobile systems. This paper studies inner and outer bounds for joint source-channel coding over Gaussian sensor networks, to drive power-distortion metrics for path planning problems for sensor data gathering. The Gaussian multiple access channel is considered for two source models. In the first setting, the underlying source is estimated with minimum mean squared error (MSE), while in the second, reconstruction of a random field is considered. The second problem simplifies to weighted MSE minimization over the sensor measurements. For both cases, we identify conditions for optimality of uncoded communication, beyond the known optimality results. For both problem settings, we derive inner and outer bounds of sensor power-distortion curve. Next, we consider optimal power allocation among sensors under a total weighted sum power constraint and obtain closed form characterizations of optimal total power versus distortion tradeoff. We numerically analyze the gap between outer and inner bounds for both total power and individual power constrained settings.