New techniques for construction of polar (sub)codes with large kernels were suggested:
- Methods for assessing the reliability of bit subchannels of the polarizing transformation, which allow one to select the indices of frozen symbols.
- Constructions of polar subcodes with large kernels with improved distance properties compared to classical polar codes.
- Methods for constructions of large polarization kernels, including kernels with the record rate of polarization and length-compatible kernels.
New decoding methods for polar (sub)codes with large kernels were proposed:
- Kernel processing algorithms, which compute the log-likelihood ratios for kernel input symbols, as required by the successive cancellation decoding method. Window and recursive trellis methods were suggested, which have the lowest complexity among the presently known approaches.
- A sequential decoding algorithm for polar codes with large kernels.
Joint application of the proposed construction and decoding methods for polar subcodes with large kernels allows one to obtain both better performance and lower decoding complexity compard to similar codes with Arikan kernel.