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This paper investigates the belief propagation decoding of spatially-coupledMacKay-Neal (SC-MN) codes over erasure channels with memory. We show that SC-MNcodes with bounded degree universally achieve the symmetric information rate(SIR) of arbitrary erasure channels with memory. We mean by universality thefollowing sense: the sender does not need to know the whole channel statisticsbut needs to know only the SIR, while the receiver estimates the transmittedcodewords from channel statistics and received words. The proof is based onpotential function.

Spatially-Coupled MacKay-Neal Codes Universally Achieve the Symmetric Information Rate of Arbitrary Generalized Erasure Channels with Memory