Polar-coded multiple-input multiple-output systems are investigated. An advanced receiver implementing joint list decoding of polar codes and QR- and MMSE-based detectors is proposed. The approximate and exact path metrics are derived for joint list decoder of polar codes. A construction of polar subcodes for MIMO systems with cross-antenna dynamic freezing constraints is proposed. The obtained polar subcodes provide significant performance gain compared to LDPC-coded MIMO systems with the same rate allocation.

Novel reduced complexity soft-input soft-output decoding algorithms for first-order Reed-Muller codes are proposed. They are based on modified fast Hadamard transform and have lower decoding complexity compared to the recursive approaches.

A reduced complexity symbolwise maximum a posteriori probability (MAP) decoding algorithm for linear block codes is presented. This algorithm is based on the recursive trellises and performs two passes over the recursion tree. Probability-domain and Log-Max implementations are considered. Numeric results show that the proposed method has lower complexity compared to other known recursive algorithms and the classical BCJR algorithm. The complexity analysis for random codes is provided.

A reduced complexity algorithm is presented for computing the log-likelihood ratios (LLRs) arising in the successive cancellation (SC) decoder for polar codes with large kernels of arbitrary dimension. The proposed algorithm exploits a recursive trellis representation of the codes generated by submatrices of the polarization kernel and enables polar codes based on large kernels to be decoded with lower complexity compared to the codes based on the Arıkan kernel with the same performance. Extensions to the case of non-binary kernels are presented.

A reduced complexity SISO decoder of linear block codes is presented. This method is based on recursive trellises and uses Hartmann-Rudolph transform. Probability- and log-domain sign-magnitude implementations are derived. Numeric results demonstrate substantial complexity reduction compared to the recursive SISO and BCJR algorithms.

A novel SISO decoding algorithm for linear block codes is presented. This algorithm is based on the recursive trellises and performs two passes over the recursion tree. Probabilitydomain implementation and its LogMax approximation are considered. Numeric results show that proposed method has lower complexity compared to the other known recursive algorithms and the classical BCJR algorithm.