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 . 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.