We consider ad hoc sensor network topologies that aim for distributed delivery of correlated delay-sensitive data. In order for efficient data delivery, network coding technique in conjunction with approximate decoding algorithm is deployed. The approximate decoding algorithm enables receivers to recover the original source data even when the number of received data packets is not sufficient for decoding. Therefore, it leads to significantly improved decoding performance and enhanced robustness for delay-sensitive data. In this paper, we further improve the approximate decoding algorithm by explicitly considering the characteristics of the correlation. Specifically, we study the case where the source data are correlated by a simple linear correlation, which is quantified by a similarity factor. We investigate several properties of the proposed algorithm and analyze the impact of the similarity factor on the decoding performance. Our experimental results confirm the properties of the proposed approximate decoding algorithm with linear correlation.