  We present a low-complexity and low-latency decoding algorithm for a class of
Reed-Muller (RM) subcodes that are defined based on the product of smaller RM
codes. More specifically, the input sequence is shaped as a multi-dimensional
array, and the encoding over each dimension is done separately via a smaller RM
encoder. Similarly, the decoding is performed over each dimension via a
low-complexity decoder for smaller RM codes. The proposed construction is of
particular interest to low-capacity channels that are relevant to emerging
low-rate communication scenarios. We present an efficient soft-input
soft-output (SISO) iterative decoding algorithm for the product of RM codes and
demonstrate its superiority compared to hard decoding over RM code components.
The proposed coding scheme has decoding (as well as encoding) complexity of
$\mathcal{O}(n\log n)$ and latency of $\mathcal{O}(\log n)$ for blocklength
$n$. This research renders a general framework toward efficient decoding of RM
codes.
