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The following topics were dealt with: properties of codes; feedback and cooperation in networks; channel coding, communication techniques and estimation methods; construction, analysis and decoding of LDPC codes; sequences and permutations; universal lossless compression; capacity and coding for fading channels; network theory; statistical mechanics; turbo and turbo-like code constructions; communication...
Identifying codes have been used in a variety of applications, including sensor-based wireless location detection in harsh environments. In such applications, a user determines his location through a unique signature (i.e. a codeword in an identifying code) based on sensor transmissions that he can hear. Adding sensors to such a system can increase its robustness at the expense of added signal interference...
The basis for designing error-correcting codes for two dimensional signal sets is considered in this paper. Both, algebraic and graph-theoretical approaches are employed in this research for establishing the fundamentals of these codes. We give a solution to the t-dominating set problem in a subfamily of degree four circulant graphs which directly provides perfect codes over the Gaussian integers...
An efficient message-passing algorithm for computing the Bayesian Cramer-Rao bound (BCRB) for general estimation problems is presented. The BCRB is a lower bound on the mean squared estimation error. The algorithm operates on a cycle-free factor graph of the system at hand. It can be applied to estimation in (1) general state-space models; (2) coupled state-space models and other systems that are...
The problem of reconstructing an unknown and unique signed permutations from their distorted patterns is considered in the paper. The set of signed permutations with the reversal metric is investigated. The reversal metric is defined as the minimal number of reversals (inversions of permutation intervals with replacing signs) which are needed to transform one permutation into another. It is proved...
Loss networks are a class of resource-sharing models which provide a powerful tool to the analysis and design of many communications and networking systems. For most loss networks of practical interest calculating the exact blocking probabilities is a difficult task. In this paper we present a new framework based on probabilistic graphical models to tackle this task. Specifically, we propose to use...
It has been shown that the stable fixed points of belief propagation (BP) algorithms correspond to extrema of the Bethe free energy. In this paper, we describe the dual problem for the minimization of the Bethe free energy and solve it using simple nonlinear block Gauss-Seidel and Jacobi algorithms. The use of the nonlinear block Gauss-Seidel algorithm corresponds to serial scheduling for the BP algorithm...
It is now well known that the performance of a linear code Copf under iterative decoding on a binary erasure channel (and other channels) is determined by the size of the smallest stopping set in the Tanner graph for Copf. Several recent papers refer to this parameter as the stopping distance s of Copf. This is somewhat of a misnomer since the size of the smallest stopping set in the Tanner graph...
A search algorithm for stopping sets in a Tanner graph is proposed for designing good low-density parity-check (LDPC) codes. By applying the belief-propagation algorithm with messages containing the information of originated variable nodes and their connected edges, the stopping sets can be detected. Furthermore, a code design method using the algorithm is presented and the performances of the designed...
We define multilevel codes on bipartite graphs which have properties analogous to multilevel serial concatenations. A linear-time decoding algorithm is described that corrects a proportion of errors equal to half the Blokh-Zyablov bound. The error probability of this algorithm has exponent similar to that of serially concatenated multilevel codes, i.e. equals the best-known exponent achievable by...
We consider the design and analysis of generalized low-density parity-check (GLDPC) codes specified by a bipartite Tanner graph, as with standard LDPC codes, but with the single parity-check constraints replaced by general coding constraints. In particular, we consider imposing Hadamard code constraints at the check nodes for a low-rate approach, termed LDPC-Hadamard codes. The achievable capacity...
In this paper we deal with codes identifying sets of vertices in random graphs, that is l-identifying codes. These codes enable us to detect sets of faulty processors in a multiprocessor system, assuming that the maximum number of faulty processors is bounded by a fixed constant l. The l-identifying codes or simply identifying codes are of special interest. For random graphs we use the model G(n,p),...
Recent work has related the belief propagation algorithm for probabilistic inference problem to some approximations to the free energy function in statistical physics. In this paper we investigate some properties of one such approximation, called the Bethe-Kikuchi approximation. We also derive low-complexity upper and lower bounds on the partition function, i.e. the global normalization constant,...
A bound on network coding rates is developed that generalizes an edge-cut bound on routing rates. The bound involves progressively removing edges from a network graph and checking whether certain strengthened d-separation conditions are satisfied. The bound improves on the cut-set bound, and its efficacy is demonstrated by showing that routing is rate-optimal for some commonly cited examples in the...
We propose a wide class of distillation schemes for multi-partite entangled states that are CSS-states. Our proposal provides not only superior efficiency, but also new insights on the connection between CSS-states and bipartite graph states. We then consider the applications of our distillation schemes for two cryptographic tasks - namely, (a) conference key agreement and (b) quantum sharing of classical...
We present a method to combine error-correction coding and spectral-efficient modulation for transmission over the additive white Gaussian noise (AWGN) channel. The code employs signal shaping which can provide a so-called shaping gain. The code belongs to the family of sparse graph codes for which efficient decoding algorithms can be derived. Simulation results show that the performance of the code...
This paper provides a construction method for low-rate low density parity check codes. Inspired by recently proposed accumulate-repeat-accumulate (ARA) codes, and hybrid concatenated codes, in this paper we extend the construction to low rates. Such codes can be viewed as hybrid concatenations of simple modules such as accumulators, repetition codes, differentiators, and punctured single parity check...
We construct a protograph-based rate-compatible family of low-density parity-check (LDPC) codes that cover a very wide range of rates from 1/2 to 16/17, perform within about 0.5 dB of their capacity limits for all rates, and can be decoded conveniently and efficiently with a common hardware implementation. In contrast to alternative methods that create codes of different rates by puncturing, shortening,...
Let NF;(n, k, r) denote the maximum number of columns in an n-row matrix with entries in a finite field F in which each column has at most r nonzero entries and every k columns are linearly independent over F. Such sparse parity check matrices are fundamental tools in coding theory, derandomization and complexity theory. We obtain near-optimal theoretical upper bounds for NF(n, k, r) in the important...
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