Low-density graph codes that are optimal for source/channel coding and binning

We describe and analyze the joint source/channel coding properties of a class of sparse graphical codes based on compounding a low-density generator matrix (LDGM) code with a low-density parity check (LDPC) code. Our first pair of theorems establish that there exist codes from this ensemble, with all degrees remaining bounded independently of block length, that are simultaneously optimal as both source and channel codes when encoding and decoding are performed optimally. More precisely, in the context of lossy compression, we prove that finite degree constructions can achieve any pair (R, D) on the rate-distortion curve of the binary symmetric source. In the context of channel coding, we prove that finite degree codes can achieve any pair (C, p) on the capacity-noise curve of the binary symmetric channel. Next, we show that our compound construction has a nested structure that can be exploited to achieve the WynerZiv bound for source coding with side information (SCSI), as well as ...

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Martin J. Wainwright, Emin Martinian
• Keywords: CORR 2007, Education, Graphical Codes, Sparse Graphical Codes, finite Degree