104 research outputs found
Algebraic approaches to distributed compression and network error correction
Algebraic codes have been studied for decades and have extensive applications in communication and storage systems. In this dissertation, we propose several novel algebraic approaches for distributed compression and network error protection problems.
In the first part of this dissertation we propose the usage of Reed-Solomon codes for compression of two nonbinary sources. Reed-Solomon codes are easy to design and offer natural rate adaptivity. We compare their performance with multistage LDPC codes and show that algebraic soft-decision decoding of Reed-Solomon codes can be used effectively under certain correlation structures. As part of this work we have proposed a method that adapts list decoding for the problem of syndrome decoding. This in turn allows us to arrive at improved methods for the compression of multicast network coding vectors. When more than two correlated sources are present, we consider a correlation model given by a system of linear equations. We propose a transformation of correlation model and a way to determine proper decoding schedules. Our scheme allows us to exploit more correlations than those in the previous work and the simulation results confirm its better performance.
In the second part of this dissertation we study the network protection problem in the presence of adversarial errors and failures. In particular, we consider the usage of network coding for the problem of simultaneous protection of multiple unicast connections, under certain restrictions on the network topology. The proposed scheme allows the sharing of protection resources among multiple unicast connections. Simulations show that our proposed scheme saves network resources by 4%-15% compared to the protection scheme based on simple repetition codes, especially when the number of primary paths is large or the costs for establishing primary paths are high
Protection against link errors and failures using network coding
We propose a network-coding based scheme to protect multiple bidirectional
unicast connections against adversarial errors and failures in a network. The
network consists of a set of bidirectional primary path connections that carry
the uncoded traffic. The end nodes of the bidirectional connections are
connected by a set of shared protection paths that provide the redundancy
required for protection. Such protection strategies are employed in the domain
of optical networks for recovery from failures. In this work we consider the
problem of simultaneous protection against adversarial errors and failures.
Suppose that n_e paths are corrupted by the omniscient adversary. Under our
proposed protocol, the errors can be corrected at all the end nodes with 4n_e
protection paths. More generally, if there are n_e adversarial errors and n_f
failures, 4n_e + 2n_f protection paths are sufficient. The number of protection
paths only depends on the number of errors and failures being protected against
and is independent of the number of unicast connections.Comment: The first version of this paper was accepted by IEEE Intl' Symp. on
Info. Theo. 2009. The second version of this paper is submitted to IEEE
Transactions on Communications (under minor revision). The third version of
this paper has been accepted by IEEE Transactions on Communication
Overlay Protection Against Link Failures Using Network Coding
This paper introduces a network coding-based protection scheme against single
and multiple link failures. The proposed strategy ensures that in a connection,
each node receives two copies of the same data unit: one copy on the working
circuit, and a second copy that can be extracted from linear combinations of
data units transmitted on a shared protection path. This guarantees
instantaneous recovery of data units upon the failure of a working circuit. The
strategy can be implemented at an overlay layer, which makes its deployment
simple and scalable. While the proposed strategy is similar in spirit to the
work of Kamal '07 & '10, there are significant differences. In particular, it
provides protection against multiple link failures. The new scheme is simpler,
less expensive, and does not require the synchronization required by the
original scheme. The sharing of the protection circuit by a number of
connections is the key to the reduction of the cost of protection. The paper
also conducts a comparison of the cost of the proposed scheme to the 1+1 and
shared backup path protection (SBPP) strategies, and establishes the benefits
of our strategy.Comment: 14 pages, 10 figures, accepted by IEEE/ACM Transactions on Networkin
Improved Compression of Network Coding Vectors Using Erasure Decoding and List Decoding
Practical random network coding based schemes for multicast include a header in each packet that records the transformation between the sources and the terminal. The header introduces an overhead that can be significant in certain scenarios. In previous work, parity check matrices of error control codes along with error decoding were used to reduce this overhead. In this work we propose novel packet formats that allow us to use erasure decoding and list decoding. Both schemes have a smaller overhead compared to the error decoding based scheme, when the number of sources combined in a packet is not too small
Protection against link errors and failures using network coding in overlay networks
We propose a network-coding based scheme to protect multiple bidirectional unicast connections against adversarial errors and failures in a network. The end nodes of the bidirectional connections are connected by a set of shared protection paths that provide the redundancy required for protection. Suppose that ne paths are corrupted by an omniscient, computationally unbounded adversary. Under our proposed protocol, the errors can be corrected at all the end nodes with 4ne protection paths. More generally, if there are ne adversarial errors and nƒ failures, 4ne + 2nƒ protection paths are sufficient. The number of protection paths only depends on the number of errors and failures being protected against and is independent of the number of unicast connections
Triazidotris[μ-2-(2-pyridyl)ethanolato]dicobalt(II) acetonitrile monosolvate
In the title compound, [Co2(C7H8NO)3(N3)3]·CH3CN, the two CoII ions in the dinuclear complex have different coordination environments, both in a distorted octahedral geometry. One CoII atom is coordinated by three O atoms from the three 2-hydroxyethylpyridine (HEP) bridging ligands, two N atoms from two HEP ligands and one azido ligand, while the other CoII atom is coordinated by the same three O atoms, one N atom from an HEP ligand and two azido ligands. Weak intermolecular C—H⋯N hydrogen bonds link the dinuclear complexes into corrugated layers parallel to the bc plane. These layers are further packed with the formation of channels propagating in [010] and filled with the disordered [in a ratio 0.691 (13):0.309 (13)] acetonitrile solvate molecules
Dichlorido{1-[(2-hydroxyethyl)iminomethyl]-2-naphtholato}pyridineiron(III) pyridine monosolvate
In the title complex, [Fe(C13H12NO2)Cl2(C5H5N)]·C5H5N, the iron(III) atom is six-coordinated by the N and O atoms from the Schiff base ligand, the N atom from a pyridine molecule and two chloride anions in a distorted octahedral geometry. The crystal packing is stabilized by intermolecular O—H⋯N hydrogen bonds and C—H⋯π interactions
Algebraic codes for Slepian-Wolf code design
Practical constructions of lossless distributed source codes (for the
Slepian-Wolf problem) have been the subject of much investigation in the past
decade. In particular, near-capacity achieving code designs based on LDPC codes
have been presented for the case of two binary sources, with a binary-symmetric
correlation. However, constructing practical codes for the case of non-binary
sources with arbitrary correlation remains by and large open. From a practical
perspective it is also interesting to consider coding schemes whose performance
remains robust to uncertainties in the joint distribution of the sources.
In this work we propose the usage of Reed-Solomon (RS) codes for the
asymmetric version of this problem. We show that algebraic soft-decision
decoding of RS codes can be used effectively under certain correlation
structures. In addition, RS codes offer natural rate adaptivity and performance
that remains constant across a family of correlation structures with the same
conditional entropy. The performance of RS codes is compared with dedicated and
rate adaptive multistage LDPC codes (Varodayan et al. '06), where each LDPC
code is used to compress the individual bit planes. Our simulations show that
in classical Slepian-Wolf scenario, RS codes outperform both dedicated and
rate-adaptive LDPC codes under -ary symmetric correlation, and are better
than rate-adaptive LDPC codes in the case of sparse correlation models, where
the conditional distribution of the sources has only a few dominant entries. In
a feedback scenario, the performance of RS codes is comparable with both
designs of LDPC codes. Our simulations also demonstrate that the performance of
RS codes in the presence of inaccuracies in the joint distribution of the
sources is much better as compared to multistage LDPC codes.Comment: 5 pages, accepted by ISIT 201
Bis[2-(pyridin-2-yl)ethanol-κ2 N,O]bis(thiocyanato-κN)nickel(II)
In the title complex, [Ni(NCS)2(C7H9NO)2], the NiII atom is in a distorted octahedral coordination environment defined by two N atoms of the two thiocyanate ions and by the N and O atoms of the two chelating 2-(pyridin-2-yl)ethanol ligands. The complex molecule is located around a crystallographic inversion center. In the crystal, molecules are connected into a two-dimensional polymeric structure parallel to (100) by O—H⋯S hydrogen bonds
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