This paper proposes a reliable data dissemination framework for edge networks, leveraging network coding combined with low-rank approximation. We consider an edge network that consists of a server and power-limited mobile devices, where the data is broadcasted by the server. In such networks, broadcasted data may be lost due to poor channel conditions or the interference incurred by the mobility of edge mobile devices, particularly without a retransmission mechanism. This can cause application errors in edge devices, lower the Quality of Service (QoS), and compromise network stability. To overcome these challenges, we propose a framework for reliable edge networks in broadcasting without retransmissions. The edge network reliability can be achieved by the approximate decoding of broadcasted data. In the proposed framework, the edge server employs matrix factorization to encode data with principal components, ensuring a lower decoding error rate even with potential packet losses. Furthermore, the proposed framework can shift the computational complexity from mobile edge devices to the edge server based on the low-rank approximation at the decoding stage, effectively mitigating power limitations on mobile devices. Through theoretical analysis, we demonstrate that the proposed algorithm outperforms typical broadcasting in terms of decoding accuracy, and present an upper bound error rate for the proposed algorithm. The simulation results confirm that the proposed algorithm outperforms other state-of-the-art algorithms in terms of decoding accuracy, time delay, and complexity.