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The base station-mobile device communication traffic has dramatically increased recently due to mobile data, which in turn heavily overloaded the underlying infrastructure. To decrease Base Station (BS) interaction, intra-cell communication between local devices, known as Device-to-Device, is utilized for distributed data caching. Nevertheless, due to the continuous departure of existing nodes and the arrival of newcomers, the missing cached data may lead to permanent data loss. In this study, we propose and analyze a class of LDPC codes for distributed data caching in cellular networks. Contrary to traditional distributed storage, a novel repair algorithm for LDPC codes is proposed which is designed to exploit the minimal direct BS communication. To assess the versatility of LDPC codes and establish performance comparisons to classic coding techniques, novel theoretical and experimental evaluations are derived. Essentially, the theoretical/numerical results for repair bandwidth cost in presence of BS are presented in a distributed caching setting. Accordingly, when the gap between the cost of downloading a symbol from BS and from other local network nodes is not dramatically high, we demonstrate that LDPC codes can be considered as a viable fault-tolerance alternative in cellular systems with caching capabilities for both low and high code rates.