Source coding with side information using list decoding

Existing literature on source coding with side information (SCSI) uses channel codes like LDPC codes and turbo codes and assumes classical unique decoding. In this paper, in contrast to classical decoding, we have taken the list decoding approach and show that the theoretical limit of SCSI can then be achieved. 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 with a few CRC bits. The CRC bits, which allow the decoder to identify the correct sequence, incur negligible overhead for large block length. More importantly, these CRC bits are not subject to noise 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.