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In this paper, we propose a scheme for distributed source coding of correlated sources using a single systematic LDPC code. In particular, since we are interested in wireless sensor network applications, we consider LDPC codes with short to moderate lengths that achieve every arbitrary coding rate on the Slepian-WoIf rate region. We simplify the distributed source coding problem to the rate-compatible LDPC code design with an unequal error protection property. The decoders communicate to each other to exchange information bits prior to decoding. However, thereafter, each performs the decoding independently. Therefore, errors in one decoder do not affect the other one. The simulation results confirm that the gap from the theoretical limit remains almost the same for different rates on the Slepian- Wolf rate region. First, we consider two correlated sources. We show that our proposed scheme improves the performance of distributed source coding of two sources considerably. This benefit is more stressed for application with short to moderate length sequences. Then, we study distributed source coding of three sources. As a special case, we investigate three sources that are pairwise correlated with the same correlation probability. We show that the gap from the theoretical limit is smaller than that of previous work. We also investigate the distributed source coding of correlated sources when there is no prior knowledge of the correlation parameter at the time of code design. We note that although the proposed distributed source coding is well suited for sensor networks (where sequences with less than 10000 bits are used), the method can be generalized to other distributed source coding applications. [ABSTRACT FROM AUTHOR]

This correspondence introduces two-dimensional (2-D) filter bank codes (TDFBCs). The synthesis bank of a two-channel two-dimensional filter bank over a finite field is used to design the 2-D code, and the corresponding analysis bank is used to generate the syndrome of the code. First, we study the encoder of half-rate TDFBCs and show that these linear codes are lattice-cyclic. It is proven that any 2-D lattice-cyclic code can also be generated by a 2-D filter bank. Second, we introduce a methodology to design TDFBCs over binary erasure channels. These codes have a simple and efficient maximum-likelihood (ML) decoding algorithm for burst erasures. We show that half-rate TDFBCs of dimensions N1 x N2 can recover burst erasures of size up to N1 x N2 /2 and N1 /2 x N2 using the proposed decoding technique. Finally, we present examples of TDFBCs that satisfy the Reiger bound with equality, i.e., they are capable of correcting any burst of size N1 N2 /2. [ABSTRACT FROM AUTHOR]