  We consider private information retrieval (PIR) for distributed storage
systems (DSSs) with noncolluding nodes where data is stored using a non maximum
distance separable (MDS) linear code. It was recently shown that if data is
stored using a particular class of non-MDS linear codes, the MDS-PIR capacity,
i.e., the maximum possible PIR rate for MDS-coded DSSs, can be achieved. For
this class of codes, we prove that the PIR capacity is indeed equal to the
MDS-PIR capacity, giving the first family of non-MDS codes for which the PIR
capacity is known. For other codes, we provide asymmetric PIR protocols that
achieve a strictly larger PIR rate compared to existing symmetric PIR
protocols.
