  In this paper, faulty successive cancellation decoding of polar codes for the
binary erasure channel is studied. To this end, a simple erasure-based fault
model is introduced to represent errors in the decoder and it is shown that,
under this model, polarization does not happen, meaning that fully reliable
communication is not possible at any rate. Furthermore, a lower bound on the
frame error rate of polar codes under faulty SC decoding is provided, which is
then used, along with a well-known upper bound, in order to choose a
blocklength that minimizes the erasure probability under faulty decoding.
Finally, an unequal error protection scheme that can re-enable asymptotically
erasure-free transmission at a small rate loss and by protecting only a
constant fraction of the decoder is proposed. The same scheme is also shown to
significantly improve the finite-length performance of the faulty successive
cancellation decoder by protecting as little as 1.5% of the decoder.
