High-Rate Regenerating Codes Through Layering

In this paper, we provide explicit constructions for a class of exact-repair regenerating codes that possess a layered structure. These regenerating codes correspond to interior points on the storage-repair-bandwidth tradeoff, and compare very well in comparison to scheme that employs space-sharing between MSR and MBR codes. For the parameter set $(n,k,d=k)$ with $n < 2k-1$, we construct a class of codes with an auxiliary parameter $w$, referred to as canonical codes. With $w$ in the range $n-k < w < k$, these codes operate in the region between the MSR point and the MBR point, and perform significantly better than the space-sharing line. They only require a field size greater than $w+n-k$. For the case of $(n,n-1,n-1)$, canonical codes can also be shown to achieve an interior point on the line-segment joining the MSR point and the next point of slope-discontinuity on the storage-repair-bandwidth tradeoff. Thus we establish the existence of exact-repair codes on a point other than the MSR and the MBR point on the storage-repair-bandwidth tradeoff. We also construct layered regenerating codes for general parameter set $(n,k<d,k)$, which we refer to as non-canonical codes. These codes also perform significantly better than the space-sharing line, though they require a significantly higher field size. All the codes constructed in this paper are high-rate, can repair multiple node-failures and do not require any computation at the helper nodes. We also construct optimal codes with locality in which the local codes are layered regenerating codes.Comment: 20 pages, 9 figure

An Improved Outer Bound on the Storage-Repair-Bandwidth Tradeoff of Exact-Repair Regenerating Codes

In this paper we establish an improved outer bound on the storage-repair-bandwidth tradeoff of regenerating codes under exact repair. The result shows that in particular, it is not possible to construct exact-repair regenerating codes that asymptotically achieve the tradeoff that holds for functional repair. While this had been shown earlier by Tian for the special case of $[n,k,d]=[4,3,3]$ the present result holds for general $[n,k,d]$. The new outer bound is obtained by building on the framework established earlier by Shah et al.Comment: 14 page

Codes With Hierarchical Locality

In this paper, we study the notion of {\em codes with hierarchical locality} that is identified as another approach to local recovery from multiple erasures. The well-known class of {\em codes with locality} is said to possess hierarchical locality with a single level. In a {\em code with two-level hierarchical locality}, every symbol is protected by an inner-most local code, and another middle-level code of larger dimension containing the local code. We first consider codes with two levels of hierarchical locality, derive an upper bound on the minimum distance, and provide optimal code constructions of low field-size under certain parameter sets. Subsequently, we generalize both the bound and the constructions to hierarchical locality of arbitrary levels.Comment: 12 pages, submitted to ISIT 201

An Alternate Construction of an Access-Optimal Regenerating Code with Optimal Sub-Packetization Level

Given the scale of today's distributed storage systems, the failure of an individual node is a common phenomenon. Various metrics have been proposed to measure the efficacy of the repair of a failed node, such as the amount of data download needed to repair (also known as the repair bandwidth), the amount of data accessed at the helper nodes, and the number of helper nodes contacted. Clearly, the amount of data accessed can never be smaller than the repair bandwidth. In the case of a help-by-transfer code, the amount of data accessed is equal to the repair bandwidth. It follows that a help-by-transfer code possessing optimal repair bandwidth is access optimal. The focus of the present paper is on help-by-transfer codes that employ minimum possible bandwidth to repair the systematic nodes and are thus access optimal for the repair of a systematic node. The zigzag construction by Tamo et al. in which both systematic and parity nodes are repaired is access optimal. But the sub-packetization level required is $r^k$ where $r$ is the number of parities and $k$ is the number of systematic nodes. To date, the best known achievable sub-packetization level for access-optimal codes is $r^{k/r}$ in a MISER-code-based construction by Cadambe et al. in which only the systematic nodes are repaired and where the location of symbols transmitted by a helper node depends only on the failed node and is the same for all helper nodes. Under this set-up, it turns out that this sub-packetization level cannot be improved upon. In the present paper, we present an alternate construction under the same setup, of an access-optimal code repairing systematic nodes, that is inspired by the zigzag code construction and that also achieves a sub-packetization level of $r^{k/r}$.Comment: To appear in National Conference on Communications 201

Cerebral Vein Thrombosis Misdiagnosed and Mismanaged

Cerebral venous thrombosis (CVT) should be considered in the differential diagnosis of all unexplained CNS disorders of sudden onset. Etiological factors are often subclinical forms of several common thrombophilic states occurring together, rather than the typical inherited and rare causes. Diagnosis is missed because of the heterogeneity in clinical presentation and etiological factors. In several patients with the so called idiopathic CVT nutritional deficiencies and lifestyle issues are more important factors in pathogenesis, rather than single rarer causes. High index of suspicion is the key to diagnosis. Clinical skill has to be fine tuned to diagnose the problem and to identify all the etiological factors. Radiology is essential for diagnosis but relying on radiology alone will lead to missing several cases and even erroneous diagnosis. It is inappropriate to proceed prematurely to laboratory investigations, forgetting proper clinical evaluation by studying diet, lifestyle, and environment of the patients. Success in managing lies in identifying all the contributory causes and correcting all of them giving excellent outcome almost always. Clinical observations based on case series and sharing of such information alone are the means to arrive at a consensus in diagnosis and management

Prevalence, severity, causes and drugs used for depression, stress and anxiety among junior doctors in a tertiary care teaching hospital in South India

Background: Due to various reasons, junior doctors experience high level of stress in their workplace. However, very few studies have been done to analyze the stress levels and pertinent causative factors among junior doctors in India. So the present study was done to investigate the prevalence, severity and causes of depression, stress and anxiety among junior doctors along with the drugs used to mitigate them.Methods: A cross sectional, questionnaire based study was conducted on a total of 114 junior doctors who include 80 interns and 34 post graduates belonging to  2013-14 batch, utilizing the 21-item depression, anxiety and stress scale (DASS 21). A personal interview was also conducted to enquire into the causes responsible for the stress and the medications employed by them to overcome it.Results: Among the interns, the mean depression score was 5.64±3.85, mean anxiety score was 6.69±3.86 and mean stress score was 7.33±3.22. Among the post graduates, the mean depression score was 4.73±2.15, mean anxiety score was 5.18±3.19 and mean stress score was 7.82±2.68. The percentage of junior doctors who had severe or extremely severe scores of depression was 11.40%, anxiety was 40.35% and stress was 9.65%. Alcohol was the most commonly used psychotropic drug (60.87%). Frequent calls during night duties and late working hours were the leading causes for stress among junior doctors.Conclusions: Overall higher stress was observed among post graduates compared to interns and females compared to males. Anxiety was more severe compared to depression and stress among junior doctors. Reducing working hours and increasing workplace flexibility are some measures to reduce stress among the junior doctors