An algebraic approach to source coding with side information using list decoding

TL;DR

This paper introduces an algebraic list decoding approach for source coding with side information, achieving theoretical limits with minimal overhead using CRC symbols, and provides design guidelines for various source types.

Contribution

It proposes a novel algebraic list decoding framework for SCSI that reaches theoretical limits and offers practical design guidelines for different source alphabets.

Findings

Achieves SCSI theoretical limits with list decoding.

CRC symbols enable correct sequence recovery with negligible overhead.

Provides design guidelines for Reed Solomon and BCH codes.

Abstract

Existing literature on source coding with side information (SCSI) mostly uses the state-of-the-art channel codes namely LDPC codes, turbo codes, and their variants and assume classical unique decoding. In this paper, we present an algebraic approach to SCSI based on the list decoding of the underlying channel codes. We show that the theoretical limit of SCSI can be achieved in the proposed list decoding based framework when the correlation between the source and side information is $q$-ary symmetric. 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 symbols. The CRC symbols, which allow the decoder to identify the correct sequence, incur negligible overhead for large block lengths. More importantly, these CRC symbols 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 for non-binary and binary sources using Reed Solomon codes and BCH codes, respectively. This guideline allows us to design a SCSI scheme for any arbitrary $q$-ary symmetric correlation without resorting to simulation.