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Asymptotic performance analysis of protograph LDPC-coded STBC systems in fading channels

In this paper, we investigate the performance of the protograph low-density parity-check (LDPC) codes concatenated with space-time block code (STBC) over Rayleigh fading channels. We firstly extend the modified protograph extrinsic information transfer (PEXIT) algorithm in order to analyze the convergence performance of protograph codes. Based on the extended PEXIT algorithm and Gaussian approximation, we further derive the asymptotic bit-error-rate (BER) expression of protograph codes. Utilizing the PEXIT algorithm, theoretical and simulated BERs, we compare the performance of two classical protograph codes, i.e., accumulate-repeat-by-3-accumulate (AR3A) code and accumulate-repeat-by-4-jagged-accumulate (AR4JA) code, regular LDPC code, and optimized irregular LDPC codes, and illustrate that the AR3A code is superior to other three codes. Additionally, we discuss the impact of the number of receive antennas (i.e., NR) on the system performance and verify that the theoretical analyses hold as NR varies. As a result, the AR3A code stands out as a good candidate for wireless communication applications with multiple antennas.