An Incremental Redundancy Hybrid ARQ Scheme.pdf

3964 IEEE TRANSACTIONS MUNICATIONS, VOL. 63, NO. 11, NOVEMBER 2015 An Incremental Redundancy Hybrid ARQ Scheme via Puncturing and Extending of Polar Codes Hamid Saber, Student Member, IEEE , and Ian Marsland, Member, IEEE Abstract —We construct polar codes for the speci?c purpose of incremental redundancy hybrid automatic repeat request (IR-HARQ) schemes. The patibility of our scheme is ensured by both puncturing and extending of the code. A new puncturing algorithm for polar codes is proposed, and we develop an algorithm for ?nding good extending sequences for polar codes from any arbitrary punctured rate, with the goal of improving the throughput as much as possible. Simulation results for differ- ent types of puncturing and extending algorithms are presented. We show how the proposed extending algorithm, when properly operated with a good puncturing algorithm and a well-chosen puncturing rate, yields IR-HARQ coding schemes which can op- erate within 1 dB of Shannon capacity over a very wide range of signal-to-noise ratios. Index Terms —Incremental redundancy hybrid ARQ, rate- compatible polar codes, channel polarization. I. I NTRODUCTION T RANSMISSION schemes for munication should provide ?exible transmission rates pensate for channel state variations. One approach is to have several pairs of encoders and decoders with different ?xed rates to adapt to the channel state. Howe