On the polar codes for MIMO

Polarization, first introduced by Arikan, is a phenomenon that after some processing of a channel, the resulted channels are either almost clean channels or useless channels. In this paper we propose three schemes to polarize a MIMO channel and design the corresponding polar codes. In the first two schemes, the MIMO channel is decomposed into different independent channels, while in the third scheme, we analyze the performance to polarize the MIMO channel directly. In SCHEME ONE, we design corresponding polar code for each independent channel, and in SCHEME TWO, we propose a method to transmit messages cooperatively in these channels. Based on the theoretical analysis and the simulation results, the SCHEME TWO can achieve a lower frame error rate without sacrifice of coding rate and decoding delay.