Encoding and Decoding of Polar Codes for Frequency Selective Fading Channels

Abstract

The polar code has attracted much attention because it has been adopted as the coding scheme for control channels of the fifth-generation mobile communications (5G) and beyond. In the encoding process, some information bits that are likely to be incorrectly decoded are selected as the frozen bits and fixed to a certain value. Almost all conventional schemes carry out this selection on the assumption of the additive white Gaussian noise (AWGN) channel. To improve the decoding performance, a conventional belief propagation (BP) decoder bit-flips some decoded bits belonging to the critical set (CS). CS is a set of indices of which information bits are not the frozen bits but tend to be incorrectly decoded. However, the combination of these conventional encoding and decoding schemes may incur degradation of block error rate (BLER) over frequency selective fading channels, because channel state information (CSI) is not considered at all. To alleviate the BLER degradation, this paper proposes a joint encoding and decoding scheme of the polar code that take into account CSI on orthogonal frequency-division multiplexing (OFDM) transmission. Firstly, the BP decoder of the proposed scheme calculates likelihood ratios (LRs) of the information bits from LRs of the received sequence, on the basis of the CSI during the estimation period. Secondly, some information bits are assigned to the frozen bits on the criterion of the absolute values of their log LRs (LLRs). Information on the frozen bits is fed back to the encoder. Thirdly, some information bits excluding the frozen bits are assigned to CS on the same criterion during the decoding period. Finally, the bits belonging to CS are bit-flipped in ascending order of reliability. Computer simulations of OFDM transmission over a multipath channel demonstrate that the proposed assignment of the frozen bits can gain average E<inf>b</inf> /N<inf>0</inf> of 3 dB over the conventional one at the same average BLER, and that the proposed assignment of CS outperforms the conventional one while reducing an amount of computational complexity by 75&#x0025;.