Polar-Coded GFDM Systems

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. INDEX TERMSPolar codes, GFDM modulation, two-stage channel transform, BICM, MLC.

A Nonuniform-Quantized Successive Cancellation Decoding of Polar Codes Over AWGN Channels

“…is obtained by (17) and the UBs of BEP for asymmetric and symmetric even NQSC decodings are obtained by (20) and (22), respectively. To avoid the case that UB is larger than 1, the UB is determined as min{1, calculated UB}.…”

“…obtained by solving the problem in (17) under the assumption that all-zero codeword is transmitted due to the symmetry of quantization levels and then the remaining boundary value Algorithm 5 : Iterative coarse-to-fine search algorithm of QB values and the information set I for symmetric odd and even nonuniform quantization levels by minimizing UB of BEP…”

“…Then, after the QBsr Q−2 are obtained by (17), the remaining r Q/2−1 and the information set I over AWGN channel are determined by solvinĝ…”

“…To adjust the output values m Q of quantizer suitable for the message values m q of quantized SC decoder, m Q is scaled as q (φ, ω) ∈ M q be the message symbol and b (s) (φ, ω) be the bit-decision (0 or 1) of the node ω in the node group φ at the stage s in the quantized SC decoder as explained in Section II-D. Hereafter, the bit-decision b (s) (φ, ω) is represented in the message form rather than 0 or 1, i.e., 0 and 1 are represented by m max q and m min q , respectively, and if there is no information before being determined, the bit-decision is expressed as 0. At the quantizer, each received value y i of a received vector y = y N −1 0 is mapped to a quantized message symbol m Q by using the quantization functions (8), (9), and (10) based on the QB values obtained by solving (17), (20), and ( 22), i.e., f Q (y i ) = m Q ∈ M Q . Then, the quantized message symbols of the quantizer f Q (y i ) are scaled to the input message symbols of quantized SC decoder m…”

“…Note that I is obtained by (17) or (20). For initialization of quantized SC decoding, the input message symbols m (0) q (0, i) are set by ( 23) and the bit-decisions b (0) (0, i), i = 0, 1, .…”