## LDPC Codes Can Approach the Slepian Wolf Bound for General Binary
Sources

Daniel Schonberg and Sandeep Pradhan^{1}

(Professor Kannan Ramchandran)

(DARPA) F30602-00-2-0538 and (NSF) CCR-0219722

We propose a constructive framework for distributed lossless source
coding of two binary sources that have arbitrary correlation
structures (Figure 1), i.e., not just symmetric correlation
structures of the form of Y = X + N where X and N are independent. Our
proposed framework accommodates the important special case of the
absence of any correlation between the two sources, wherein it
becomes an entropy coding scheme for a single source (Figure 2).
This framework is obtained by combining Low-density
parity check (LDPC) codes with the distributed source coding
using syndromes (DISCUS) framework of [1]. This combined algorithm
is powerful enough to reach the Slepian-Wolf bound for two
memoryless binary sources and the entropy rate for a single
memoryless binary source.

Figure 1: Block diagram of symmetric DISCUS. Two sources are compressed independently and reconstructed at the receiver.

Figure 2: Symmetric DISCUS construction used for lossless coding, or in the special case of zero correlation between sources.

- [1]
- S.S. Pradhan and K. Ramchandran, "Distributed Source Coding Using Syndromes (DISCUS): Design and Construction,"
*IEEE Data Compression Conf.,* Snowbird, UT, March 1999.

^{1}Professor, University of Michigan

Send mail to the author : (dschonbe@eecs.berkeley.edu)

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