Network Error Correction for Unit-Delay, Memory-Free Networks Using Convolutional Codes

A single source network is said to be memory-free if all of the internal nodes (those except the source and the sinks) do not employ memory but merely send linear combinations of the symbols received at their incoming edges on their outgoing edges. In this work, we introduce network-error correction for single source, acyclic, unit-delay, memory-free networks with coherent network coding for multicast. A convolutional code is designed at the source based on the network code in order to correct network- errors that correspond to any of a given set of error patterns, as long as consecutive errors are separated by a certain interval which depends on the convolutional code selected. Bounds on this interval and the field size required for constructing the convolutional code with the required free distance are also obtained. We illustrate the performance of convolutional network error correcting codes (CNECCs) designed for the unit-delay networks using simulations of CNECCs on an example network under a probabilistic error model.

X-Codes: A Low Complexity Full-Rate High-Diversity Achieving Precoder for TDD MIMO Systems

We consider a time division duplex multiple-input multiple-output (nt × nr MIMO). Using channel state information (CSI) at the transmitter, singular value decomposition (SVD) of the channel matrix is performed. This transforms the MIMO channel into parallel subchannels, but has a low overall diversity order. Hence, we propose X-Codes which achieve a higher diversity order by pairing the subchannels, prior to SVD preceding. In particular, each pair of information symbols is encoded by a fixed 2 × 2 real rotation matrix. X-Codes can be decoded using nr very low complexity two-dimensional real sphere decoders. Error probability analysis for X-Codes enables us to choose the optimal pairing and the optimal rotation angle for each pair. Finally, we show that our new scheme outperforms other low complexity precoding schemes.

Implications of the half-duplex constraint on relay-aided cooperation using rateless codes

The half-duplex constraint, which mandates that a cooperative relay cannot transmit and receive simultaneously, considerably simplifies the demands made on the hardware and signal processing capabilities of a relay. However, the very inability of a relay to transmit and receive simultaneously leads to a potential under-utilization of time and bandwidth resources available to the system. We analyze the impact of the half-duplex constraint on the throughput of a cooperative relay system that uses rateless codes to harness spatial diversity and efficiently transmit information from a source to a destination. We derive closed-form expressions for the throughput of the system, and show that as the number of relays increases, the throughput approaches that of a system that uses more sophisticated full-duplex nodes. Thus, half-duplex nodes are well suited for cooperation using rateless codes despite the simplicity of both the cooperation protocol and the relays.

Explicit codes uniformly reducing repair bandwidth in distributed storage

A distributed storage setting is considered where a file of size B is to be stored across n storage nodes. A data collector should be able to reconstruct the entire data by downloading the symbols stored in any k nodes. When a node fails, it is replaced by a new node by downloading data from some of the existing nodes. The amount of download is termed as repair bandwidth. One way to implement such a system is to store one fragment of an (n, k) MDS code in each node, in which case the repair bandwidth is B. Since repair of a failed node consumes network bandwidth, codes reducing repair bandwidth are of great interest. Most of the recent work in this area focuses on reducing the repair bandwidth of a set of k nodes which store the data in uncoded form, while the reduction in the repair bandwidth of the remaining nodes is only marginal. In this paper, we present an explicit code which reduces the repair bandwidth for all the nodes to approximately B/2. To the best of our knowledge, this is the first explicit code which reduces the repair bandwidth of all the nodes for all feasible values of the system parameters.

Explicit codes minimizing repair bandwidth for distributed storage

We consider the problem of minimizing the bandwidth required to repair a failed node when data is stored across n nodes in a distributed manner, so as to facilitate reconstruction of the entire data by connecting to any k out of the n nodes. We provide explicit and optimal constructions which permit exact replication of a failed systematic node.

Single real-symbol decodable, high-rate, distributed space-time block codes

A scheme to apply the rate-1 real orthogonal designs (RODs) in relay networks with single real-symbol decodability of the symbols at the destination for any arbitrary number of relays is proposed. In the case where the relays do not have any information about the channel gains from the source to themselves, the best known distributed space time block codes (DSTBCs) for k relays with single real-symbol decodability offer an overall rate of complex symbols per channel use. The scheme proposed in this paper offers an overall rate of 2/2+k complex symbol per channel use, which is independent of the number of relays. Furthermore, in the scenario where the relays have partial channel information in the form of channel phase knowledge, the best known DSTBCs with single real-symbol decodability offer an overall rate of 1/3 complex symbols per channel use. In this paper, making use of RODs, a scheme which achieves the same overall rate of 1/3 complex symbols per channel use but with a decoding delay that is 50 percent of that of the best known DSTBCs, is presented. Simulation results of the symbol error rate performance for 10 relays, which show the superiority of the proposed scheme over the best known DSTBC for 10 relays with single real-symbol decodability, are provided.

Constant pressure laminar, transitional and turbulent flows - An approximate unified treatment

A nondimensional number that is constant in two-dimensional, incompressible and constant pressure laminar and fully turbulent boundary, layer flows has been proposed. An extension of this to constant pressure transitional flow is discussed.

Reaction of La2CuO4 with binary metal oxides in the solid state: Metathesis, addition, and redox metathesis pathways

Investigation of the reaction of La2CuO4 with several binary metal oxides in the solid state at elevated temperatures has revealed three different reaction pathways. Reaction of La2CuO4 with strongly acidic oxides such as Re2O7, MoO3, and V2O5 follows a metathesis route, yielding a mixture of products: La3ReO8/La2MoO6/LaVO4 and CuO. Oxides such as TiO2, MnO2, and RuO2 which are not so acidic yield addition products: La2CuMO6 (M = Ti, Mn, Ru). SnO2 is a special case which appears to follow a metathesis route, giving La2Sn2O7 pyrochlore and CuO, which on prolonged reaction transform to the layered perovskite La2CuSnO6. The reaction of La2CuO4 with lower valence oxides VO2 and MoO2, on the other hand, follows a novel redox metathesis route, yielding a mixture of LaVO4/LaCuO2 and La2MoO6/Cu, respectively. This result indicates that it is the redox reactivity involving V-IV + Cu-II --> V-V + Cu-I and Mo-IV + Cu-II --> Mo-VI + Cu-0, and not the acidity of the binary oxide, that controls the nature of the products formed in these cases. The general significance of these results toward the synthesis of complex metal oxides containing several metal atoms is discussed.

Scaling analysis of momentum, heat, and mass transfer in binary alloy solidification problems

A systematic approach is developed for scaling analysis of momentum, heat and species conservation equations pertaining to the case of solidification of a binary mixture. The problem formulation and description of boundary conditions are kept fairly general, so that a large class of problems can be addressed. Analysis of the momentum equations coupled with phase change considerations leads to the establishment of an advection velocity scale. Analysis of the energy equation leads to an estimation of the solid layer thickness. Different regimes corresponding to different dominant modes of transport are simultaneously identified. A comparative study involving several cases of possible thermal boundary conditions is also performed. Finally, a scaling analysis of the species conservation equation is carried out, revealing the effect of a non-equilibrium solidification model on solute segregation and species distribution. It is shown that non-equilibrium effects result in an enhanced macrosegregation compared with the case of an equilibrium model. For the sake of assessment of the scaling analysis, the predictions are validated against corresponding computational results.

Dielectric anomaly in strontium borate-bismuth vanadate glass nanocomposite

Transparent glass nanocomposites in the pseudo binary system (100 - x) SrB4O7 (SBO)-x Bi2VO5.5 (BiV) (0 less than or equal to n less than or equal to 70) were prepared by the splat quenching technique. The nano-crystallization of bismuth vanadate (BiV) in 50 SBO-50 BiV (in mol%) glass composite has been demonstrated. These were characterized for their structural, thermal and dielectric properties. As-quenched composites under study have been confirmed to be amorphous by X-ray powder diffraction (XRD) studies. The glass transition temperature (T-g) and crystallization temperatures (T-er) were determined using differential thermal analyses (DTA), High resolution transmission electron microscopic (HRTEM) studies carried out on heat-treated samples reveal the presence of spherical nanosize crystallites of Bi2VO5.5 (BiV) dispersed in the glassy matrix of SrB4O7 (SSO). The dielectric constant (epsilon (r)) and the dielectric loss (D) measurements were carried out on the as-quenched and heat-treated glass nanocomposite samples in the frequency range 100 Hz-10 MHz. The as-quenched and the heat-treated at two different temperatures (720 and 820 K) samples exhibited broad dielectric anomalies in the vicinity of the ferroelectric-to-paraelectric transition temperature of the parent BiV ceramics. The Curie-Weiss law was found to be valid at a temperature above the transition temperature, establishing the diffused nature of the transition. (C) 2001 Elsevier Science Ltd. All rights reserved.

Axisymmetric turbulent boundary layer along a circular cylinder at constant pressure

A constant-pressure axisymmetric turbulent boundary layer along a circular cylinder of radius a is studied at large values of the frictional Reynolds number a+ (based upon a) with the boundary-layer thickness δ of order a. Using the equations of mean motion and the method of matched asymptotic expansions, it is shown that the flow can be described by the same two limit processes (inner and outer) as are used in two-dimensional flow. The condition that the two expansions match requires the existence, at the lowest order, of a log region in the usual two-dimensional co-ordinates (u+, y+). Examination of available experimental data shows that substantial log regions do in fact exist but that the intercept is possibly not a universal constant. Similarly, the solution in the outer layer leads to a defect law of the same form as in two-dimensional flow; experiment shows that the intercept in the defect law depends on δ/a. It is concluded that, except in those extreme situations where a+ is small (in which case the boundary layer may not anyway be in a fully developed turbulent state), the simplest analysis of axisymmetric flow will be to use the two-dimensional laws with parameters that now depend on a+ or δ/a as appropriate.

Three-dimensional double-diffusive convection and macrosegregation during non-equilibrium solidification of binary mixtures

A three-dimensional transient mathematical model (following a fixed-grid enthalpy-based continuum formulation) is used to study the interaction of double-diffusive natural convection and non-equilibrium solidification of a binary mixture in a cubic enclosure cooled from a side. Investigations are carried out for two separate test systems, one corresponding to a typical model "metal-alloy analogue" system and other corresponding to a real metal-alloy system. Due to stronger effects of solutal buoyancy in actual metal-alloy systems than in corresponding analogues, the convective transport mechanisms for the two cases are quite different. However, in both cases, similar elements of three-dimensionality are observed in the curvature and spacing of the projected streamlines. As a result of three-dimensional convective flow patterns, a significant solute macrosegregation is observed across the transverse sections of the cavity, which cannot be captured by two-dimensional simulations. (C) 2003 Elsevier Science Ltd. All rights reserved.