An Adaptive IR-HARQ Scheme for Polar Codes by Polarizing Matrix Extension

Abstract

In this letter, we construct rate compatible polar codes via polarizing matrix extension, to support efficient adaptive incremental redundancy hybrid automatic repeat request (IR-HARQ) protocol. We show that an arbitrary number of incremental coded bits can be generated by extending the polarizing matrix, such that multiple retransmissions are aggregated to produce a longer polar code with extra coding gain. This coding gain is maximized by selecting the most reliable bit channels in the extended codes, rather than the shorter codes, as information bits. Naturally, some information bits are transferred from the shorter part to the extended part for higher bit channel reliability. One-to-one parity-checking between the two parts lends itself well to the above purpose during the construction of the longer code. Simulation results demonstrate consistent coding gain over the chase combining HARQ scheme.