Design of Rate-Compatible Parallel Concatenated Punctured Polar Codes for IR-HARQ Transmission Schemes  
[PERSON]  
1 Communication Engineering Research Centre, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China; [EMAIL_ADDRESS] (J.J.); [EMAIL_ADDRESS] (S.W. ); [EMAIL_ADDRESS] (B.F.); [EMAIL_ADDRESS] (S.G.)  
[PERSON]  
1 Communication Engineering Research Centre, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China; [EMAIL_ADDRESS] (J.J.); [EMAIL_ADDRESS] (S.W. ); [EMAIL_ADDRESS] (B.F.); [EMAIL_ADDRESS] (S.G.)  
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[PERSON]  
1 Communication Engineering Research Centre, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China; [EMAIL_ADDRESS] (J.J.); [EMAIL_ADDRESS] (S.W. ); [EMAIL_ADDRESS] (B.F.); [EMAIL_ADDRESS] (S.G.)  
2  
[PERSON]  
3 Communication Engineering Research Centre, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China; [EMAIL_ADDRESS] (J.J.); [EMAIL_ADDRESS] (S.W. ); [EMAIL_ADDRESS] (B.F.); [EMAIL_ADDRESS] (S.G.)  
2  
[PERSON]  
1 Communication Engineering Research Centre, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China; [EMAIL_ADDRESS] (J.J.); [EMAIL_ADDRESS] (S.W. ); [EMAIL_ADDRESS] (B.F.); [EMAIL_ADDRESS] (S.G.)  
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Footnote 1: email: {[EMAIL_ADDRESS], [EMAIL_ADDRESS], jay@hit. One approach is to have several pairs of different code-rate encoders and decoders to adapt to the channel variations [19]. However, this requires extra coding complexity. As an alternative, a popular solution to compensate for channel state variations is incremental redundancy hybrid automatic repeat request (IR-HARQ) [20; 21; 22], where the parity bits are sent in an incremental fashion depending on the quality of the time-varying channel. In this way, the rate-compatible (RC) codes are well-suited for the IR-HARQ scheme to address the scalable code-rate requirement, which can be implemented with a single encoder/decoder pair. Therefore, if decoding is not successful at a particular rate, then the receiver can request only the additional parity bits from the transmitter, instead of the full set of parity bits of the code with a lower rate. Although polar codes can achieve the capacity of any binary memoryless symmetric channel, which is natural to be applied to IR-HARQ transmission schemes [23], their RC constructions are not in general capacity-achieving due to the limitation of the block length of conventional polar codes being restricted to a power of two. In general, a family of RC polar codes typically obtained by puncturing, where the set of parity bits of a code with a higher rate is a subset of the set of parity bits of a code with a lower rate. The study of puncturing patterns for polar codes to obtain arbitrary block lengths and code-rates are considered in [24; 25; 26; 27]. However, puncturing of polar codes incurs a loss of performance, and the performance of these punctured codes are worse than the conventional polar codes even if they have the same length and code rate. Authors in [28] proposed an efficient polar coding scheme for optimizing jointly the puncturing patterns and the set of information bits of the polar code, and showed that it outperformed the LDPC codes defined in WiMAX standard. Moreover, the puncturing patterns in [25; 26; 27; 28] are optimized according to the set of information bits, these methods cannot be used to design a family of RC punctured codes for IR-HARQ, which requires the same information set that should be used for all punctured codes from a mother code in the family. Consider the heuristic search algorithm presented in [24], which developed a good puncturing pattern for a fixed information set. Therefore, in order to determine an optimal RC puncturing patterns, one needs to consider the trade-offs between complexity and reliability [29; 30; 31], which is still an open problem. Recently, Refs. [32; 33] have proposed RC polar-like codes that are provably capacity-achieving over any class of a degraded family of channels.