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Regenerating code is a class of code very suitable for distributed storagesystems, which can maintain optimal bandwidth and storage space. Two types ofimportant regenerating code have been constructed: the minimum storageregeneration (MSR) code and the minimum bandwidth regeneration (MBR) code.However, in hostile networks where adversaries can compromise storage nodes,the storage capacity of the network can be significantly affected. In thispaper, we propose two optimal constructions of regenerating codes throughrate-matching that can combat against this kind of adversaries in hostilenetworks: 2-layer rate-matched regenerating code and $m$-layer rate-matchedregenerating code. For the 2-layer code, we can achieve the optimal storageefficiency for given system requirements. Our comprehensive analysis shows thatour code can detect and correct malicious nodes with higher storage efficiencycompared to the universally resilient regenerating code which is astraightforward extension of regenerating code with error detection andcorrection capability. Then we propose the $m$-layer code by extending the2-layer code and achieve the optimal error correction efficiency by matchingthe code rate of each layer's regenerating code. We also demonstrate that theoptimized parameter can achieve the maximum storage capacity under the sameconstraint. Compared to the universally resilient regenerating code, our codecan achieve much higher error correction efficiency.

Optimal Construction of Regenerating Code through Rate-matching in Hostile Networks