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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]

This paper introduces a procedure for constructing convolutional codes using finite-field wavelets. This provides novel insight into the study of convolutional codes and permits the design of the new convolutional codes that is not possible by conventional methods. Exploiting algebraic properties of the wavelet codes, we show that a rate K/L wavelet convolutional encoder is a basic encoder that is noncatastrophic. In addition, we prove that any rate 1/L wavelet convolutional encoder is minimal-basic and that every L-band orthogonal wavelet system generates a rate 1/L self-orthogonal code. As an application of wavelet convolutional codes, we construct time-varying convolutional codes. These codes have unique trellis structures that result in fast and low computational complexity decoding algorithms. As examples, we present some time-varying wavelet convolutional codes that can be decoded faster than comparable lime-invariant convolutional codes. We construct 16- and 32-state time-varying wavelet convolutional codes with minimum-free distances of seven and eight, respectively. These codes have the same minimum-free distance as the best time-invariant codes of the same rate and state complexity, but they can be decoded almost twice as fast. We show that a 32-state time-varying wavelet convolutional code is superior to the Lauer code in performance while having almost the same decoding complexity. Although the 32-state wavelet code is inferior to the 16-state Golay convolutional code as far as computational complexity, it outperforms this code in the performance. We also prove that orthogonal filterbanks generate self-dual time-varying codes. We give a design for doubly even self-dual time-varying convolutional codes by imposing some constraints on the filters that define the L-band orthogonal wavelets. As another application of wavelet convolutional codes, we propose a new scheme for generating rate-adaptive codes. These codes have the property that multiple rates of the code can be decoded on one trellis and its subtrellises. [ABSTRACT FROM AUTHOR]