Re-polarization processing in extended polar codes

In this paper, extended polar codes based on repolarization technique are proposed. The presented schemes extend a conventional polar code of length N to length N + q, which stand in contrast to known length-compatible schemes such as puncturing and shortening techniques that reduce the length from N to N q. For certain specific lengths, the waterfall region performance of our extended polar code is superior to that of other length-compatible polar codes. It provides better reliability and reduces the management overhead in several storage devices and communications systems. In essence, extended polar codes are created by re-polarizing the q least reliable nonfrozen bit-channels with the help of q additional frozen bit-channels. It is proved that this re-polarization enhances the reliability of these bits. Moreover, the extended schemes can be not only modified to improve decoding performance, but generalized as a m-stage scheme to improve throughput significantly. With parallel operation, the throughput is improved around 2m1 times when q is small. Compared to a shortened polar code with length 1536, the encoding and decoding complexities of an extended polar code are only 50% and 60.5%, respectively.