Abstract
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.
Highlights
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)
To reduce the complexity and processing latency, the bit-interleaved coded modulation (BICM)-PC-Generalized frequency division multiplexing (GFDM) scheme is designed with the help of an interleaver, where the GFDM channel is parallel divided into a series of independent binary-input channels in the first stage channel transform
Based on the two-stage channel transform of the multilevel coding (MLC)-PCGFDM system, the optimal performance can be achieved by using a multi-stage decoding (MSD) in the receiver, where the reliability values (e.g., LLRs) corresponding to the first bit level is computed first, which is passed to the first decoder
Summary
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). Compared to the TC-GFDM system, the PC-GFDM system jointly optimizes the combination of binary polar coding and GFDM transmission Under this joint design framework, two PC-GFDM schemes, namely, MLC-PC-GFDM and BICM-PC-GFDM are proposed. We have proved that the capacities of channels corresponding to all transmitted symbols are identical, the MLC-PC-GFDM is designed to achieve the optimal performance, where the GFDM channel is serially split into a group of correlated binary-input channels in the first stage channel transform. To reduce the complexity and processing latency, the BICM-PC-GFDM scheme is designed with the help of an interleaver, where the GFDM channel is parallel divided into a series of independent binary-input channels in the first stage channel transform. At the second stage channel transform, the conventional binary channel polarization is performed for both PC-GFDM schemes. Throughout this paper, log (·) denotes ‘‘logarithm to base 2’’, and ln (·) represents the natural logarithm
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