A Note on “Signal-to-Noise Ratio Mismatch for Low-Density Parity-Check Coded Magnetic Recording Channels” by W. Tan and J. R. Cruz

In this letter, we prove that the minimum signal-to-noise ratio (SNR) threshold of the iterative belief propagation algorithm for a low-density parity-check (LDPC) coded magnetic recording channel is obtained when the SNR mismatch factor is half the ratio of variance to mean for the Gaussian distribution at the channel output. This result was first observed by Tan and Cruz empirically