Performance analysis of LDPC coded GFDM systems

Abstract

This paper analyzes the error probability performance of low‐density parity‐check (LDPC) coded generalized frequency division multiplexing (GFDM) systems over Rayleigh fading and additive white Gaussian noise (AWGN) channels. The initial log‐likelihood ratio (LLR) expressions used in the sum‐product algorithm (SPA) decoder are first derived for the system model presented in this paper. Based on the decoding threshold of the system, the frame error rate (FER) in the low Eb/N0$E_b/N_0$ region is estimated by modeling the channel variations using the observed bit error rate (BER). Then, a lower bound based on the absorbing sets is proposed for FER when quantized SPA decoders are used. For AWGN channels, the lower bound can act as an estimate of the FER in the error‐floor region if the absorbing set is dominant and its multiplicity is known. For Rayleigh channels, the lower bound can still be used to estimate the FER performance of selected codes. The estimation approach for the FER in the low Eb/N0$E_b/N_0$ region and the lower bound on the FER in the high Eb/N0$E_b/N_0$ region can be used as practical tools for evaluating different designs of GFDM‐based systems in terms of the error probability performance. The quantization scheme has an important impact on the FER and BER performances. Randomly constructed and array‐based LDPC codes are used to obtain numerical results that show the system performance and the accuracy of the proposed FER estimations.