  In this paper, we present an efficient method to construct a good
rate-compatible punctured polar (RCPP) code. One of the major challenges on the
construction of a RCPP code is to design a common information set which is good
for all the codes in the family. In the proposed construction, a common
information set is simply optimized for the highest-rate punctured polar code
in the family and then, this set is updated for each other code by satisfying
the condition that information bits are unchanged during retransmissions. This
is enabled by presenting a novel hierarchical puncturing and information-copy
technique. To be specific, some information bits are copied to frozen-bit
channels, which yields an information-dependent frozen vector. Then, the
updated information sets are obtained by appropriately combining the common
information set and an information-dependent frozen vector. Moreover, the
impact of unknown frozen bits are resolved using the proposed hierarchical
puncturing. Simulation results demonstrate that the proposed RCPP code attains
a significant performance gain (about 2dB) over a benchmark RCPP code where
both codes use the same puncturing patterns but the latter uses the
conventional all-zero frozen vector. Therefore, the proposed method would be
crucial to construct a good RCPP code.
