In most of existing Internet of Things (IoT) applications, data compression, data encryption and error/erasure correction are implemented separately. To achieve reliable communication, in particular, in harsh wireless environment with strong interference, error/erasure correction codes with higher correction capability or Automatic repeat request (ARQ) scheme are desirable but at the cost of increasing complexity and energy consumption. Due to resource-constrained IoT device, it is often challenging to implement all of them. In this paper, we propose a novel lightweight efficient secure error-robust scheme, ENCRUST, which is able to achieve these three functions using simple matrix multiplication. ENCRUST is built on the new theoretical foundation of projection-based encoding presented in this paper, by leveraging the sparsity inherent in the signal. We perform theoretical analysis and experimental study of the proposed scheme in comparison with the conventional schemes. It shows that the proposed scheme can work in low SINR range and the reconstructed signal quality shows graceful degradation. Furthermore, we apply the proposed scheme on real-life electrocardiogram (ECG) dataset and images. The results demonstrate that ENCRUST achieves decent compression, information secrecy as well as strong error recovery in one go.