Low-density constructions can achieve the Wyner-Ziv and Gelfand-Pinsker bounds

We describe and analyze sparse graphical code constructions for the problems of source coding with decoder side information (the Wyner-Ziv problem), and channel coding with encoder side information (the Gelfand-Pinsker problem). Our approach relies on a combination of low-density parity check (LDPC) codes and low-density generator matrix (LDGM) codes, and produces sparse constructions that are simultaneously good as both source and channel codes. In particular, we prove that under maximum likelihood encoding/decoding, there exist lowdensity codes (i.e., with finite degrees) from our constructions that can saturate both the Wyner-Ziv and Gelfand-Pinsker bounds.

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Emin Martinian, Martin J. Wainwright
• Keywords: Constructions, CORR 2006, Education, Low-density Generator Matrix, Sparse Graphical Code