Modified REP Pattern for 3×3 Kernel Polar Codes

Using large size kernels in conjunction with the binary kernel enables length flexibility in polar codes. However, the resultant multi-kernel polar codes suffer from high decoding complexity. The size-3 kernels have drawn much attention due to their sufficiently high polarization exponents and the lowest decoding complexity among larger than size-2 kernels. However, the two specific size-3 kernels that can achieve the optimal polarization have a zero in their last rows. This results in the error-rate performance degradation of the repetition (REP) and generalized-repetition (G-REP) nodes in addition to increased memory requirements for their fast decoders. In this letter, we propose modifications to the REP and G-REP nodes that simultaneously result in improved error-rate performance and reduced memory requirements for their fast decoders.