  We introduce successive cancellation (SC) decoding of product codes (PCs)
with single parity-check (SPC) component codes. Recursive formulas are derived,
which resemble the SC decoding algorithm of polar codes. We analyze the error
probability of SPC-PCs over the binary erasure channel under SC decoding. A
bridge with the analysis of PCs introduced by Elias in 1954 is also
established. Furthermore, bounds on the block error probability under SC
decoding are provided, and compared to the bounds under the original decoding
algorithm proposed by Elias. It is shown that SC decoding of SPC-PCs achieves a
lower block error probability than Elias' decoding.
