  The problem of source coding with side information (SCSI) is closely related
to channel coding. Therefore, existing literature focuses on using the most
successful channel codes namely, LDPC codes, turbo codes, and their variants,
to solve this problem assuming classical unique decoding of the underlying
channel code. In this paper, in contrast to classical decoding, we have taken
the list decoding approach. We show that syndrome source coding using list
decoding can achieve the theoretical limit. We argue that, as opposed to
channel coding, the correct sequence from the list produced by the list decoder
can effectively be recovered in case of SCSI, since we are dealing with a
virtual noisy channel rather than a real noisy channel. Finally, we present a
guideline for designing constructive SCSI schemes using Reed Solomon code, BCH
code, and Reed-Muller code, which are the known list-decodable codes.
