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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 $V\subset \mathbb{F}_2^m$ fromwhich $\underline{z}=\underline{y}-\underline{x}$ is uniformly chosen. Orequivalently, the receiver receives an affine subspace $\underline{y}-V$ where$\underline{x}$ lies. We consider a joint iterative decoder involving thechannel detector and the LDPC decoder. The decoding system considered in thispaper can be viewed as a simplified model of the joint iterative decoder overnon-binary modulated signal inputs e.g., $2^m$-QAM. We evaluate the performanceof binary spatially-coupled MacKay-Neal codes by density evolution. Theiterative decoding threshold is seriously degraded by increasing $m$. EXIT-likefunction curve calculations reveal that this degradation is caused by wigglesand can be mitigated by increasing the randomized window size. The resultantiterative decoding threshold values are very close to the Shannon limit.

Spatially-Coupled Binary MacKay-Neal Codes for Channels with Non-Binary Inputs and Affine Subspace Outputs