Wireless sensor networks (WSNs) have found a wide variety of applications recently. However, the challenges in WSNs still remain in improving the sensor energy efficiency and information quality (distortion reduction) of the sensing data transmissions. In this paper, we propose a novel cross-layer design of resource allocation and channel coding to protect distributed source coding (DSC)-based data transmission. Resource allocation strategies include rate adaptation and automatic repeat-request retransmissions. Our proposed joint design of resource allocation, channel coding, and DSC can improve the network energy efficiency and information quality while meeting the data transmission latency requirements. Further, we investigate how the resource allocation enables the network to achieve unequal error protection among correlated DSC streams. Our simulation studies demonstrate that the proposed joint design significantly improves the DSC-based data transmission quality and the network energy efficiency.