  Staircase codes (SCCs) are typically decoded using iterative bounded-distance
decoding (BDD) and hard decisions. In this paper, a novel decoding algorithm is
proposed, which partially uses soft information from the channel. The proposed
algorithm is based on marking certain number of highly reliable and highly
unreliable bits. These marked bits are used to improve the
miscorrection-detection capability of the SCC decoder and the error-correcting
capability of BDD. For SCCs with $2$-error-correcting BCH component codes, our
algorithm improves upon standard SCC decoding by up to $0.30$~dB at a bit-error
rate of $10^{-7}$. The proposed algorithm is shown to achieve almost half of
the gain achievable by an idealized decoder with this structure.
