In this paper, we consider the design of polar codes for point-to-point (P2P) MIMO-OFDM system with channel sparsity. We first adopt singular value decomposition (SVD) precoding to obtain a parallel symbol-wise fading channel with different effective signal-to-noise ratios (SNRs) on different subchannels due to the frequency selectivity. After a detailed evaluation on the effective SNRs, we show that the received symbols not only are corrupted by channel noise but also suffer from, effectively, channel erasure since some subchannels are in deep fade. Therefore, we propose the Reed Muller (RM)-channel degradation construction based on the statistical SNRs in achieving the balance between erasure correction and error correction abilities of polar codes via adjusting a tunable parameter. Numerical results show that a noticeable coding gain can be achieved by the proposed construction comparing with 5G polar codes.

Conventional construction of non-binary polar codes divides the synthesized channels into the frozen channels and information channels. Each information channel carries one symbol i.e.$q$bits. However, there are many middle channels with insufficient polarization, which can not carry one symbol of$q$bits but only$i$bits,$1 \leq i