  A product code with single parity-check component codes can be described via
the tools of a multi-kernel polar code, where the rows of the generator matrix
are chosen according to the constraints imposed by the product code
construction. Following this observation, successive cancellation decoding of
such codes is introduced. In particular, the error probability of single
parity-check product codes over binary memoryless symmetric channels under
successive cancellation decoding is characterized. A bridge with the analysis
of product codes introduced by Elias is also established for the binary erasure
channel. Successive cancellation list decoding of single parity-check product
codes is then described. For the provided example, simulations over the binary
input additive white Gaussian channel show that successive cancellation list
decoding outperforms belief propagation decoding applied to the code graph.
Finally, the performance of the concatenation of a product code with a
high-rate outer code is investigated via distance spectrum analysis. Examples
of concatenations performing within $0.7$ dB from the random coding union bound
are provided.
