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Design of bilayer lengthened LDPC codes for Rayleigh fading relay channels

Recently, two classes of high rate bilayer low-density parity-check (LDPC) codes have been proposed for Gaussian relay channels using bilayer density evolution technique. These two classes include bilayer lengthened LDPC codes and bilayer expurgated LDPC codes that have been used in a decode-and-forward relaying strategy. In this paper, we first study the decode-and-forward achievable rates for a Rayleigh fading relay channel. Then, we design bilayer lengthened LDPC codes for this channel model in different SNR regimes, namely, when the link between the source and the relay is much stronger than the link between the source and the destination and when the SNRs of these links are comparable.