Source Coding With Side Information Using List Decoding

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.