  This paper investigates the error probability of several decoding methods for
a source code with decoder side information, where the decoding methods are: 1)
symbol-wise maximum a posteriori decoding, 2) successive-cancellation decoding,
and 3) stochastic successive-cancellation decoding. The proof of the
effectiveness of a decoding method is reduced to that for an arbitrary decoding
method, where `effective' means that the error probability goes to zero as $n$
goes to infinity. Furthermore, we revisit the polar source code showing that
stochastic successive-cancellation decoding, as well as successive-cancellation
decoding, is effective for this code.
