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$\epsilon$-Minimum Storage Regenerating ($\epsilon$-MSR) codes form a specialclass of Maximum Distance Separable (MDS) codes, providing mechanisms for exactregeneration of a single code block in their codewords by downloading slighlysub-optimal amount of information from the remaining code blocks. The keyadvantage of these codes is a significantly lower sub-packetization that growsonly logarithmically with the length of the code, while providing optimality instorage and error-correcting capacity. However, from an implementation point ofview, these codes require each remaining code block to be available for therepair of any single code block. In this paper, we address this issue byconstructing $\epsilon$-MSR codes that can repair a failed code block bycontacting a fewer number of available code blocks. When a code block fails,our repair procedure needs to contact a few compulsory code blocks and is freeto choose any subset of available code blocks for the remaining choices.Further, our construction requiresa field size linear in code length andensures load balancing among the contacted code blocks in terms of informationdownloaded from them for a single repair.

$\epsilon$-MSR Codes: Contacting Fewer Code Blocks for Exact Repair