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.

Low-density parity-cheek (LDPC) codes, Magnetic recording channels (MRC), Signal-to-noise ratio (SNR) mismatch
dx.doi.org/10.1109/TMAG.2006.880998
IEEE Transactions on Magnetics
Department of Systems and Computer Engineering

Saeedi, H. (Hamid), & Banihashemi, A. (2006). A note on "signal-to-noise ratio mismatch for low-density parity-check coded magnetic recording channels" by W. Tan and J. R. Cruz. IEEE Transactions on Magnetics, 42(11), 3765–3766. doi:10.1109/TMAG.2006.880998