• The Journal of Korean Institute of Communications and Information Sciences
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• v.39B no.11
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• pp.723-729
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• 2014

In this paper, we derive the average repair bandwidth and/or read cost for arbitrary repairable linear code ensembles. The repair bandwidth and read cost are the required amount of data and access number of nodes to restore a failed node, respectively. Here, the repairable linear code ensemble is given by such parameters as the number k of data symbols, the number m of parity symbols, and their degree distributions. We further assume that the code is systematic, and no other constraint is assumed, except possibly that the exact repair could be done by the parity check-sum relation with fully connected n=k+m storages. This enables one to apply the result of this paper directly to any randomly constructed codes with the above parameters, such as linear fountain codes. The final expression of the average repair read cost shows that it is highly dependent on the degree distribution of parity symbols, and also the values n and k.