Computer Science – Information Theory
Scientific paper
2007-04-13
Computer Science
Information Theory
Appeared as technical report 730, Dept. of Statistics, UC Berkeley. Portions previously published in conference form (DCC 2006
Scientific paper
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 Wyner-Ziv bound for source coding with side information (SCSI), as well as the Gelfand-Pinsker bound for channel coding with side information (CCSI). Although the current results are based on optimal encoding and decoding, the proposed graphical codes have sparse structure and high girth that renders them well-suited to message-passing and other efficient decoding procedures.
Martinian Emin
Wainwright Martin J.
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