A CSI-Based Construction Scheme for GN-Coset Codes over Frequency Selective Fading Channels

Polar codes, which can be classified into G
N
-coset codes as well as Reed-Muller (RM) codes, has been applied to wireless communications. Considering that generator matrices of polar and RM codes can be obtained by selecting some row vectors from G
N
, this paper proposes a row-selection criterion for constructing G
N
-coset codes that can maintain good transmission performance of orthogonal frequency-division multiplexing (OFDM) over frequency selective fading channels while alleviating the performance degradation of RM codes with high code rate. Since the proposed criterion exploits channel state information (CSI) of the frequency selective channels, information on the selected or deleted row vectors should be fed back to the encoder. In addition, a new feedback system that aims to reduce an amount of feedback information is proposed. Computer simulations demonstrate that the proposed code construction scheme is superior to the conventional polar and RM codes in terms of block error rate (BLER) performance with a wide range of the code rate, when belief propagation (BP) based decoding is employed. Especially, the proposed scheme can achieve average E
b
/N
0
gain of 3-7 dB over the polar codes of the 5G standard. In addition, the proposed feedback system with a wide range of the code rate can reduce more than 50% of feedback information in comparison with the conventional one.