Thresholds for LDPC codes over OFDM

Low Density Parity Check (LDPC) codes have been proven to perform very close to the Shannon limit with low complexity encoders and decoders. The experimental proof of existence of codes that achieve a rate 0.0045 dB from the Shannon-capacity for Binary Input Additive White Gaussian Noise Channels (BIAWGN) is a big impetus for exploring similar codes and encoding-decoding schemes for other channels. In this work, our aim is to make fundamental comparisons between the performances of LDPC codes on an Inter-Symbol Interference (ISI) channel under two competing equalization methods — the time-domain BCJR algorithm and the frequency-domain Orthogonal Frequency Division Multiplexing (OFDM). Thresholds for LDPC codes with the BCJR algorithm have been derived and proved in prior work by Kavcic et al. In this paper, we study thresholds for LDPC codes over an OFDM system. We develop a rigorous density evolution method (without Gaussian approximations) to prove the existence of thresholds for LDPC codes over OFDM and evaluate the thresholds for various regular LDPC codes. We compare the OFDM thresholds with BCJR thresholds and draw some useful conclusions for code design.