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

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

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

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 $q$-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

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

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