  Piggybacking is an efficient method to decrease the repair bandwidth of
Maximum Distance Separable (MDS) codes or Minimum Storage Regenerating (MSR)
codes. In this paper, for minimizing the repair bandwidth of parity nodes of
the known MSR codes with high rate, which is usually the whole size of the
original data, i.e., the maximal, a new systematic piggybacking design is
proposed through an in-depth analysis of the design of piggybacking. As a
result, new MSR codes are obtained with almost optimal repair bandwidth of
parity nodes while retaining the optimal repair bandwidth of systematic nodes.
Furthermore, MSR codes with balanced download during node repair process are
presented based on the new piggybacking design.
