In this paper, we consider decoding of loss tolerant data encoded by network coding and transmitted over error-prone networks. Intermediate network nodes typically perform the random linear network coding in a Galois field and a Gaussian elimination is used for decoding process in the terminal nodes. In such settings, conventional decoding approaches can unfortunately not reconstruct any encoded data unless they receive at least as many coded packets as the original number of packets. In this paper, we rather propose to exploit the incomplete data at a receiver without major modifications to the conventional decoding architecture. We study the problem of approximate decoding for inter-dependent sources where the difference between source vectors is characterized by a unimodal distribution. We propose a mode-based algorithm for approximate decoding, where the mode of the source data distribution is used to reconstruct source data. We further improve the mode-based approximate decoding algorithm by using additional short information that is referred to as position similarity information (PSI). We analytically study the impact of PSI size on the approximate decoding performance and show that the optimal size of PSI can be determined based on performance requirements of applications. The proposed approach has been tested in an illustrative example of data collection in sensor networks. The simulation results confirm the benefits of approximate decoding for inter-dependent sources and further show that 93.3% of decoding errors are eliminated when the approximate decoding uses appropriate PSI. (C) 2015 Elsevier B.V. All rights reserved.