  We address noisy message-passing decoding of lowdensity parity-check (LDPC)
codes over additive white Gaussian noise channels. Message-passing decoders in
which certain processing units iteratively exchange messages are common for
decoding LDPC codes. The exchanged messages are in general subject to internal
noise in hardware implementation of these decoders. We model the internal
decoder noise as additive white Gaussian noise (AWGN) degrading exchanged
messages. Using Gaussian approximation of the exchanged messages, we perform a
two-dimensional density evolution analysis for the noisy LDPC decoder. This
makes it possible to track both the mean, and the variance of the exchanged
message densities, and hence, to quantify the threshold of the LDPC code in the
presence of internal decoder noise. The numerical and simulation results are
presented that quantify the performance loss due to the internal decoder noise.
To partially compensate this performance loss, we propose a simple method,
based on EXIT chart analysis, to design robust irregular LDPC codes. The
simulation results indicate that the designed codes can indeed compensate part
of the performance loss due to the internal decoder noise.
