  We study LDPC codes for the channel with $2^m$-ary input $\underline{x}\in
\mathbb{F}_2^m$ and output $\underline{y}=\underline{x}+\underline{z}\in
\mathbb{F}_2^m$. The receiver knows a subspace $V\subset \mathbb{F}_2^m$ from
which $\underline{z}=\underline{y}-\underline{x}$ is uniformly chosen. Or
equivalently, the receiver receives an affine subspace $\underline{y}-V$ where
$\underline{x}$ lies. We consider a joint iterative decoder involving the
channel detector and the LDPC decoder. The decoding system considered in this
paper can be viewed as a simplified model of the joint iterative decoder over
non-binary modulated signal inputs e.g., $2^m$-QAM. We evaluate the performance
of binary spatially-coupled MacKay-Neal codes by density evolution. The
iterative decoding threshold is seriously degraded by increasing $m$. EXIT-like
function curve calculations reveal that this degradation is caused by wiggles
and can be mitigated by increasing the randomized window size. The resultant
iterative decoding threshold values are very close to the Shannon limit.
