Low-density constructions for lossy compression, binning, and coding with side information

In this extended abstract, we provide a high-level overview of some of our recent work [10], [11], [9] on low-density graphical codes for various communication problems including lossy compression, binning, and coding with side information. Sparse graphical codes, particularly low-density parity check (LDPC) codes, are widely used and well understood in application to channel coding problems [16]. On the other hand, for other communication problems—especially those involving aspects of both channel and source coding—there remain various open questions associated with using low-density code constructions. Examples of such problems include (a) lossy source coding (data compression); (b) source coding with side information (the Wyner-Ziv problem [19]), and (c) channel coding with side information (the Gelfand-Pinsker problem [7]). Our work tackles these problems using sparse graphical constructions that are based on a combination of LDPC codes, and their dual versions, namely low-density generator matrix (LDGM) codes.