Generalized frequency division multiplexing (GFDM) is a block-based non-orthogonal multicarrier modulation scheme proposed for 5G PHY layer. In this paper, to efficiently coordinate the features of interference existing in the GFDM system, we propose a theoretical framework of the polar-coded GFDM (PC-GFDM) system, which allows jointly optimizing the combination of binary polar coding and GFDM modulation. The original GFDM channel is decomposed into multiple bit polarized channels by using a two-stage channel transform. The general modulation partition is performed in the first stage and the bit polarization transform is done in the second stage. Specifically, two schemes are considered for the first stage channel transform, multilevel coding (MLC) and bit-interleaved coded modulation (BICM). Based on the theorem we have proved in this paper that the capacities of channels corresponding to all transmitted symbols are identical, the MLC based PC-GFDM system is designed to optimize the combining of polar codes and GFDM system. Then the BICM based PC-GFDM system is designed to reduce the complexity and processing latency, which yields the suboptimal performance. Simulation results indicate that the proposed PC-GFDM systems significantly outperform the existing turbo-coded GFDM systems because of the joint design between the polar coding and the GFDM modulation.

Introduction

Polar codes proposed by Arıkan [1] are the first constructive codes that have been proved to achieve the symmetric capacity for the binary-input memoryless channels (BMCs). This capacity-achieving code family is based on a technique named channel polarization, which recently has been employed in many scenarios for signal processing. In 2013, Seidl et al. have introduced the channel polarization idea into the 2m-ary modulation scheme [2] and proposed two different polar-coded modulation (PCM) schemes, where the bit-interleaved coded modulation (BICM) [3] and multilevel coding (MLC) approaches are considered respectively. Later, by extending the channel polarization idea to non-orthogonal multiple access (NOMA) scenario, whereby the original NOMA channel is split into a set of binary-input channels under a three-stage channel transform, Dai et al design a polar-coded NOMA system [4] to jointly optimize the combination of binary polar coding, signal modulation and NOMA transmission. Similarly, polar-coded multiple-input multiple-output (MIMO) schemes [5] also have been developed to improve the system performance.