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Inspired by the recent progress in self-supervised learning for computer vision, in this paper we introduce DeLoRes, a new general-purpose audio representation learning approach. Our main objective is to make our network learn representations in a resource-constrained setting (both data and compute), that can generalize well across a diverse set of downstream tasks. Inspired from the Barlow Twins objective function, we propose to learn embeddings that are invariant to distortions of an input audio sample, while making sure that they contain non-redundant information about the sample. To achieve this, we measure the cross-correlation matrix between the outputs of two identical networks fed with distorted versions of an audio segment sampled from an audio file and make it as close to the identity matrix as possible. We use a combination of a small subset of the large-scale AudioSet dataset and FSD50K for self-supervised learning and are able to learn with less than half the parameters compared to state-of-the-art algorithms. For evaluation, we transfer these learned representations to 9 downstream classification tasks, including speech, music, and animal sounds, and show competitive results under different evaluation setups. In addition to being simple and intuitive, our pre-training algorithm is amenable to compute through its inherent nature of construction and does not require careful implementation details to avoid trivial or degenerate solutions. Furthermore, we conduct ablation studies on our results and make all our code and pre-trained models publicly available https://github.com/Speech-Lab-IITM/DeLoRes.