Interference Alignment in Regenerating Codes for Distributed Storage: Necessity and Code Constructions

Regenerating codes are a class of recently developed codes for distributed storage that, like Reed-Solomon codes, permit data recovery from any arbitrary k of n nodes. However regenerating codes possess in addition, the ability to repair a failed node by connecting to any arbitrary d nodes and downloading an amount of data that is typically far less than the size of the data file. This amount of download is termed the repair bandwidth. Minimum storage regenerating (MSR) codes are a subclass of regenerating codes that require the least amount of network storage; every such code is a maximum distance separable (MDS) code. Further, when a replacement node stores data identical to that in the failed node, the repair is termed as exact. The four principal results of the paper are (a) the explicit construction of a class of MDS codes for d = n-1 >= 2k-1 termed the MISER code, that achieves the cut-set bound on the repair bandwidth for the exact-repair of systematic nodes, (b) proof of the necessity of interference alignment in exact-repair MSR codes, (c) a proof showing the impossibility of constructing linear, exact-repair MSR codes for d < 2k-3 in the absence of symbol extension, and (d) the construction, also explicit, of MSR codes for d = k+1. Interference alignment (IA) is a theme that runs throughout the paper: the MISER code is built on the principles of IA and IA is also a crucial component to the non-existence proof for d < 2k-3. To the best of our knowledge, the constructions presented in this paper are the first, explicit constructions of regenerating codes that achieve the cut-set bound.Comment: 38 pages, 12 figures, submitted to the IEEE Transactions on Information Theory;v3 - The title has been modified to better reflect the contributions of the submission. The paper is extensively revised with several carefully constructed figures and example

Explicit Construction of Optimal Exact Regenerating Codes for Distributed Storage

Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a recent paper, Wu et al. characterize the tradeoff between the repair bandwidth and the amount of data stored per node. They also prove the existence of regenerating codes that achieve this tradeoff. In this paper, we introduce Exact Regenerating Codes, which are regenerating codes possessing the additional property of being able to duplicate the data stored at a failed node. Such codes require low processing and communication overheads, making the system practical and easy to maintain. Explicit construction of exact regenerating codes is provided for the minimum bandwidth point on the storage-repair bandwidth tradeoff, relevant to distributed-mail-server applications. A subspace based approach is provided and shown to yield necessary and sufficient conditions on a linear code to possess the exact regeneration property as well as prove the uniqueness of our construction. Also included in the paper, is an explicit construction of regenerating codes for the minimum storage point for parameters relevant to storage in peer-to-peer systems. This construction supports a variable number of nodes and can handle multiple, simultaneous node failures. All constructions given in the paper are of low complexity, requiring low field size in particular.Comment: 7 pages, 2 figures, in the Proceedings of Allerton Conference on Communication, Control and Computing, September 200

Network coding

Network coding is a technique to increase the amount of information flow in a network by making the key observation that information flow is fundamentally different from commodity flow. Whereas, under traditional methods of operation of data networks, intermediate nodes are restricted to simply forwarding their incoming message symbols downstream, network coding achieves vast performance gains by permitting intermediate nodes to carry out algebraic operations on the incoming data. In this article we present a tutorial introduction to network coding as well as an application to the efficient operation of distributed data-storage networks

Customer Satisfaction with Domestic Water Supply in India – A Study in Hubli city

Severe water crisis prevailed in twin Cities of Hubli-Dharwad in South India for a long time. During the last ten years, there has been considerable improvement in the water service. While most parts of the city is having intermittent supply system, a pilot 24/7 water service was implemented in a Demonstration Zone through the World Bank assistance, and State Government of Karnataka. The 24x7 project covers about 12 % of the total population of the city.  The objective of this paper is to study the customer satisfaction in both intermittent and 24/7 water service areas in Hubli city.  Stratified sampling method was adopted for four groups namely, low, medium, high income and backward classes namely the Scheduled Cast/Scheduled Tribes (SC/ST) groups.  The results of the study revealed that most customers in 24/7 demo zone were highly satisfied with water quality, continuity, quantity, and pressure; whereas there was slight dissatisfaction (12%) with regard to redressal of customer complaints. In contrast, there was considerable dissatisfaction with water quality, continuity and pressure in intermittent supply areas. There was universal opinion from both 24/7 demo zone and intermittent service areas supporting 24/7 water service scale up project in the city. Keywords: Intermittent Water Service, 24/7 Water Service, Customer Satisfactio

Revival of Superconductivity by Y3+/Ca2+ substitution in YBa2Cu2.7Co0.3O7 without reported phase transformation

Results of phase formation, resistivity (r), and thermo-electric power (S), are reported on Y1-xCaxBa2Cu2.7Co0.3O7 compounds with x = 0.1 and 0.2. Pristine compound i.e. without Co or Ca substitution crystallizes in orthorhombic structure with space group P/mmm. Cu-site Co substituted compound i.e. YBa2Cu2.7Co0.3O7 is tetragonal. With simultaneous doping of Ca at Y site in Co substituted compound i.e. Y1-xCaxBa2Cu2.7Co0.3O7 the tetragonal nature still remains. r(T) measurements showed superconducting transition temperature (Tc) to decrease from 90K (YBa2Cu3O7) to 33 K for YBa2Cu2.7Co0.3O7 which with further Ca substitution increases from 33K to 53K (Y0.9 Ca0.1Ba2Cu2.7Co0.3O7) and 67 K for Y0.8 Ca0.2Ba2Cu2.7Co0.3O7. Tc decreases first with Cu-site Co substitution by hole-filling and later recovers by simultaneous hole creation by Y site Ca substitution. Room temperature thermoelectric power S(300 K), which is an indirect measure of mobile carriers shows the decrease of carriers with Co doping and creation by Ca substitution. Our results demonstrate the hole filling by Co substitution is compensated by simultaneous Ca substitution.Comment: 10 pages of TEXT and Fig

Hollow Bulb Definitive Obturation of a Post-Covid Mucormycosis Maxillectomy Defect – A Case Report.

The novel Coronavirus, also known as SARS-CoV-2 (Severe Acute Respiratory Syndrome Coronavirus 2), causes COVID-19.In the wake of COVID-19, incidences of mucormycosis were rising alarmingly, especially rhino-orbital-cerebral mucormycosis.Most cases required surgical intervention followed by the fabrication of obturators.A hollow obturator is the most practical, convenient, and cost-effective solution for prosthodontic rehabilitation. A patient with pain overthe maxillary region (left) reported to the department of Prosthodontics and Crown & Bridge. His past medical history revealed that he tested and recovered from SARS-CoV-2. Clinical, radiographic, and smear tests confirmed rhino-cerebral mucormycosis with post covid pneumonia. Surgical left partial maxillectomy performed 4 months back. His intra-oral examination revealed a large maxillary defect extending from the left-sided alveolar bone, along with a missing base of the maxilla and palatal bone.The case report presents a hollow bulb definitive obturator fabrication for the treatment of acquired maxillary defects after COVID-19-caused mucormycosis