Partially collaborative storage codes in the presence of an eavesdropper

We consider the study of codes designed for distributed storage systems, whose maintenance design criterion is to reduce the repair bandwidth, in a generic setting where t failures are repaired collaboratively, thus involving the participation of t storage nodes. Yet each of these t nodes is actually actively exchanging data with only a subset of the nodes, explaining the term 'partially collaborating'. To understand the role of the different code parameters, namely the threshold t of failures, the degree s of collaboration, but also the repair bandwidth, we adopt the general scenario where an eavesdropper may spy on some storage nodes, and their communication links. By doing so, we recover previous results on partially collaborative codes, and discuss some aspects of cooperation and security in terms of their influence on the repair bandwidth in the presence of an eavesdropper.