  In this paper, we present a sparse neural network decoder (SNND) of polar
codes based on belief propagation (BP) and deep learning. At first, the
conventional factor graph of polar BP decoding is converted to the bipartite
Tanner graph similar to low-density parity-check (LDPC) codes. Then the Tanner
graph is unfolded and translated into the graphical representation of deep
neural network (DNN). The complex sum-product algorithm (SPA) is modified to
min-sum (MS) approximation with low complexity. We dramatically reduce the
number of weight by using single weight to parameterize the networks. Optimized
by the training techniques of deep learning, proposed SNND achieves comparative
decoding performance of SPA and obtains about $0.5$ dB gain over MS decoding on
($128,64$) and ($256,128$) codes. Moreover, $60 \%$ complexity reduction is
achieved and the decoding latency is significantly lower than the conventional
polar BP.
