  We describe a novel approach to interpret a polar code as a low-density
parity-check (LDPC)-like code with an underlying sparse decoding graph. This
sparse graph is based on the encoding factor graph of polar codes and is
suitable for conventional belief propagation (BP) decoding. We discuss several
pruning techniques based on the check node decoder (CND) and variable node
decoder (VND) update equations, significantly reducing the size (i.e., decoding
complexity) of the parity-check matrix. As a result, iterative polar decoding
can then be conducted on a sparse graph, akin to the traditional
well-established LDPC decoding, e.g., using a fully parallel sum-product
algorithm (SPA). This facilitates the systematic analysis and design of polar
codes using the well-established tools known from analyzing LDPC codes. We show
that the proposed iterative polar decoder has a negligible performance loss for
short-to-intermediate codelengths compared to Arikan's original BP decoder.
Finally, the proposed decoder is shown to benefit from both reduced complexity
and reduced memory requirements and, thus, is more suitable for hardware
implementations.
