Performance Analysis of LDPC Codes with Maximum-Ratio Combining Cascaded with Selection Combining over Nakagami-m Fading

Low-density parity-check (LDPC) codes combined with cascade combining are able to achieve excellent bit-error rate (BER) performance over multipath fading channels. Cascade combining, which involves two stages of diversity combining, is very useful for situations where site diversity exists and it can reduce the complexity of the combiner when the number of diversity branches increases. The average output signal-to-noise ratio and the uncoded BER expressions of cascade combining over independent and identically distributed (i.i.d.) Nakagami-m fading channels are derived. The BER expressions of cascade combining with LDPC codes over i.i.d. Nakagami-m fading channels are derived based on the Gaussian approximation (GA) approach. These expressions include selection combining and maximum-ratio combining as special cases. The signal-to-noise ratio (SNR) thresholds for error-free decoding are obtained using density evolution (DE). Comparisons among GA analysis, DE analysis, and simulations show that they are in good agreement. The expressions obtained from the GA analysis provide better theoretical understanding of the system performance and allow us to compute the BER and SNR threshold more efficiently as compared to DE and simulations. Lastly, the stability conditions for GA and DE analyses, which are found to be exactly the same, are also presented.