On iterative performance of LDPC and Root-LDPC codes over block-fading channels

This paper¹ presents our investigation on iterative decoding performances of some sparse-graph codes on block-fading Rayleigh channels. The considered code ensembles are standard LDPC codes and Root-LDPC codes, first proposed in [1] and shown to be able to attain the full transmission diversity. We study the iterative threshold performance of those codes as a function of fading gains of the transmission channel and propose a numerical approximation of the iterative threshold versus fading gains, both both LDPC and Root-LDPC codes. Also, we show analytically that, in the case of 2 fading blocks, the iterative threshold γ^*_root of Root-LDPC codes is proportional to (α₁α₂)^-1, where α₁ and α₂ are corresponding fading gains. From this result, the full diversity property of Root-LDPC codes immediately follows.