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57
Codes and Decoding on General Graphs
, 1996
"... Iterative decoding techniques have become a viable alternative for constructing high performance coding systems. In particular, the recent success of turbo codes indicates that performance close to the Shannon limit may be achieved. In this thesis, it is showed that many iterative decoding algorithm ..."
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Cited by 354 (1 self)
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Iterative decoding techniques have become a viable alternative for constructing high performance coding systems. In particular, the recent success of turbo codes indicates that performance close to the Shannon limit may be achieved. In this thesis, it is showed that many iterative decoding algorithms are special cases of two generic algorithms, the minsum and sumproduct algorithms, which also include noniterative algorithms such as Viterbi decoding. The minsum and sumproduct algorithms are developed and presented as generalized trellis algorithms, where the time axis of the trellis is replaced by an arbitrary graph, the "Tanner graph". With cyclefree Tanner graphs, the resulting decoding algorithms (e.g., Viterbi decoding) are maximumlikelihood but suffer from an exponentially increasing complexity. Iterative decoding occurs when the Tanner graph has cycles (e.g., turbo codes); the resulting algorithms are in general suboptimal, but significant complexity reductions are possible compared to the cyclefree case. Several performance estimates for iterative decoding are developed, including a generalization of the union bound used with Viterbi decoding and a characterization of errors that are uncorrectable after infinitely many decoding iterations.
LH*RS  a highavailability scalable distributed data structure
"... (SDDS). An LH*RS file is hash partitioned over the distributed RAM of a multicomputer, e.g., a network of PCs, and supports the unavailability of any of its k ≥ 1 server nodes. The value of k transparently grows with the file to offset the reliability decline. Only the number of the storage nodes p ..."
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Cited by 59 (11 self)
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(SDDS). An LH*RS file is hash partitioned over the distributed RAM of a multicomputer, e.g., a network of PCs, and supports the unavailability of any of its k ≥ 1 server nodes. The value of k transparently grows with the file to offset the reliability decline. Only the number of the storage nodes potentially limits the file growth. The highavailability management uses a novel parity calculus that we have developed, based on the ReedSalomon erasure correcting coding. The resulting parity storage overhead is about the minimal ever possible. The parity encoding and decoding are faster than for any other candidate coding we are aware of. We present our scheme and its performance analysis, including experiments with a prototype implementation on Wintel PCs. The capabilities of LH*RS offer new perspectives to data intensive applications, including the emerging ones of grids and of P2P computing.
Wireless LANs and Mobile Networking: Standards and Future Directions
, 1996
"... this paper, we discuss several emerging standards that relate to wireless LAN systems. These standards include two physical and link layer standards, IEEE 802.11 and ETSI HIPERLAN, as well as a mobile networking standard, Mobile IP, and some developing standards for wireless link management. In this ..."
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Cited by 37 (2 self)
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this paper, we discuss several emerging standards that relate to wireless LAN systems. These standards include two physical and link layer standards, IEEE 802.11 and ETSI HIPERLAN, as well as a mobile networking standard, Mobile IP, and some developing standards for wireless link management. In this paper, we focus on the use of radio frequency wireless LANs, as opposed to infrared wireless systems. For radio frequency wireless LANs, the availability of
A Frame Construction and A Universal Distortion Bound for Sparse Representations
"... We consider approximations of signals by the elements of a frame in a complex vector space of dimension N and formulate both the noiseless and the noisy sparse representation problems. The noiseless representation problem is to find sparse representations of a signal r given that such representatio ..."
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Cited by 35 (2 self)
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We consider approximations of signals by the elements of a frame in a complex vector space of dimension N and formulate both the noiseless and the noisy sparse representation problems. The noiseless representation problem is to find sparse representations of a signal r given that such representations exist. In this case, we explicitly construct a frame, referred to as the Vandermonde frame, for which the noiseless sparse representation problem can be solved uniquely using O(N²) operations, as long as the number of nonzero coefficients in the sparse representation of r is ɛN for some 0 ≤ ɛ ≤ 0.5. It is known that ɛ ≤ 0.5 cannot be relaxed without violating uniqueness. The noisy sparse representation problem is to find sparse representations of a signal r satisfying a distortion criterion. In this case, we establish a lower bound on the tradeoff between the sparsity of the representation, the underlying distortion and the redundancy of any given frame.
Completely transitive codes in Hamming graphs
, 1998
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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Cited by 18 (2 self)
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Tensorbased Trapdoors for CVP and their Application to Public Key Cryptography
, 2000
"... . We propose two trapdoors for the ClosestVectorProblem in lattices (CVP) related to the lattice tensor product. Using these trapdoors we set up a latticebased cryptosystem which resembles to the McEliece scheme. 1 Keywords. Public Key Cryptosystem, Closest Vector Problem, Lattice Reduction ..."
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Cited by 10 (0 self)
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. We propose two trapdoors for the ClosestVectorProblem in lattices (CVP) related to the lattice tensor product. Using these trapdoors we set up a latticebased cryptosystem which resembles to the McEliece scheme. 1 Keywords. Public Key Cryptosystem, Closest Vector Problem, Lattice Reduction, Trapdoor, McEliece 1 Introduction Since the invention of public key cryptography in 1976 by Di#e and Hellman [DH76] security of most cryptosystems is based on the (assumed) hardness of factoring or computing discrete logarithms. Only a few schemes based on other problems remain unbroken. Among which there is the McEliece scheme [St95] based on the computational di#culty of decoding a random code. It is still a challenge to develop new public key cryptosystem originating from the hardness of non numbertheoretic problems. In a pioneer work Ajtai [A96] constructed an e#ciently computable function which is hard to invert on the average if the underlying lattice problem is intractable in th...
Minimum distance bounds by graph analysis
 IEEE Trans. Inform. Theory
, 2001
"... The paritycheck matrix of a linear code is used to define a bipartite code constraint (Tanner) graph in which bit nodes are connected to parity check nodes. The connectivity properties of this graph are analyzed using both local connectivity and the eigenvalues of the associated adjacency matrix. A ..."
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Cited by 10 (1 self)
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The paritycheck matrix of a linear code is used to define a bipartite code constraint (Tanner) graph in which bit nodes are connected to parity check nodes. The connectivity properties of this graph are analyzed using both local connectivity and the eigenvalues of the associated adjacency matrix. A simple lower bound on minimum distance of the code is expressed in terms of the two largest eigenvalues. For a more powerful bound, local properties of the subgraph corresponding to a minimum weight word in the code are used to create an optimization problem whose solution is a lower bound on the code’s minimum distance. Linear programming gives one bound. The technique is illustrated by applying it to sparse block codes with parameters [7,3,4] and [42,23,6].
Improving the Performance of Spatial Watermarking of Images Using Channel Coding
"... In this paper we present a spatialdomain watermarking scheme for data hiding and copyright protection of still images and analyze the effect that the application of channel coding has on the performance of the watermark detection and decoding tests. Detector structures are derived for both tests an ..."
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Cited by 9 (3 self)
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In this paper we present a spatialdomain watermarking scheme for data hiding and copyright protection of still images and analyze the effect that the application of channel coding has on the performance of the watermark detection and decoding tests. Detector structures are derived for both tests and analytical bounds and approximations are obtained for the bit error rate (BER) and the receiver operating characteristic (ROC) associated with the watermark decoding and detection tests when block codes are employed. Finally, the analytical expressions are contrasted with experimental results in several cases of interest. 1 Introduction The representation of images in digital format allows the use of communication networks and electronic media to efficiently store, distribute and manipulate visual information. However, these resources can also be applied to illegally manipulate and redistribute digital information at low cost. Therefore, the use of communication networks such as Internet...