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In this paper, we present an efficient method to construct a good rate-compatible punctured polar (RCPP) code for incremental redundancy hybrid automatic repeat request schemes. One of the major challenges on the construction of a RCPP code is to optimize a common information set which is good for all the (punctured) polar codes in the family. Unfortunately, there is no efficient way to solve the above problem. In the proposed construction, a common information set is simply optimized for the highest-rate code in the family and then it is updated to yield an effective information set for each other code, by keeping the condition that information bits are unchanged during retransmissions. This is enabled by presenting a novel hierarchical (or reciprocal) puncturing and information-copy technique. Specifically, some information bits are copied to frozen-bit channels whose locations are carefully determined according to rate-compatible puncturing patterns. This yields an information-dependent frozen vector in the encoding part. Also, in the decoding part, the effective information sets are obtained by properly combining the common information set and the information-dependent frozen vector. More importantly, the impact of unknown frozen bits are avoided due to the special structure of the proposed hierarchical (or reciprocal) puncturing. Simulation results verify that the proposed RCPP code can yield a significant performance gain (about 2 dB) over a benchmark RCPP code where both codes use the same rate-compatible 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 efficiently.

An Efficient Construction of Rate-Compatible Punctured Polar (RCPP) Codes Using Hierarchical Puncturing