The universality of LDPC codes on correlated fading channels with decision feedback based receiver

This paper proves that low density parity check (LDPC) codes are universal codes on correlated fading channels if a successive decoding receiver is used. A universal LDPC code is defined as a code with the same performance over a class of channels, in which the performance is measured by the threshold of the code in terms of mutual information (in bits/sec/Hz). The receiver proposed in this paper decomposes the fading channel into a bank of memoryless sub-channels. Each sub-channel is encoded with a LDPC code. An MMSE estimator followed by a LDPC decoder is used to successively decodes the channel code. With this scheme, we show that LDPC codes have the universal performance on fading channels with variant fading rates. We also prove that the LDPC code design is unified. Hence, the optimal LDPC codes for the perfect CSI receiver is also optimal for correlated fading channels without CSI.