  Recently, the research on local repair codes is mainly confined to repair the
failed nodes within each repair group. But if the extreme cases occur that the
entire repair group has failed, the local code stored in the failed group need
to be recovered as a whole. In this paper, local codes with cooperative repair,
in which the local codes are constructed based on minimum storage regeneration
(MSR) codes, is proposed to achieve repairing the failed groups. Specifically,
the proposed local codes with cooperative repair construct a kind of mutual
interleaving structure among the parity symbols, that the parity symbols of
each local code, named as distributed local parity, can be generated by the
parity symbols of the MSR codes in its two adjacent local codes. Taking
advantage of the structure given, the failed local groups can be repaired
cooperatively by their adjacent local groups with lower repair locality, and
meanwhile the minimum distance of local codes with cooperative repair is
derived. Theoretical analysis and simulation experiments show that, compared
with codes with local regeneration (such as MSR-local codes and MBR-local
codes), the proposed local codes with cooperative repair have benefits in
bandwidth overhead and repair locality for the case of local groups failure.
