We study the exact and optimal repair of multiple failures in codes for distributed storage. More particularly, we provide an explicit construction of exact minimum bandwidth coordinated regenerating codes (MBCR) for n = d + t, k, d ≥ k, t ≥ 1. Our construction differs from existing constructions by allowing both t > 1 (i.e., repair of multiple failures) and d > k (i.e., contacting more than k ...

In this work, we give locally repairable regenerating code (LRRC) [1]–[4] constructions that can protect the file size promised by the graph analysis of the modified family helper selection (MFHS) scheme [1] at the minimum-bandwidthregenerating (MBR) point. I. RANDOM LINEAR CODE CONSTRUCTION FOR A CLASS OF (n, k, d, r) PARAMETERS In this section, we prove the existence and construction of linea...

Regenerating codes based on the approach of interference alignment for wireless interference channel achieve the cut-set bound for distributed storage systems. These codes provide data reliability, and perform efficient exact node repair when some node fails. Interference alignment as a concept is especially important to improve the repair efficiency of a failed node in a minimum storage regene...

abstract in this paper, the effect of foreign sector macro-variable on inflation dynamics and firms’ pricing behavior has been investigated in the context of a small open economy new keynesian phillips curve. this curve is derived and estimated for a developing oil-exporting economy suffering from dutch disease. this version of nkpc is an extension of leith and malley’s (2007) small open econom...

Fractional repetition (FR) codes is a family of codes for distributed storage systems that allow for uncoded repair having the minimum repair bandwidth. However, in contrast to minimum bandwidth regenerating codes, where a random set of certain size of available nodes is used for a node repair, the repairs with FR codes are table based. In this work we consider bounds on the fractional repetiti...

We address the open problem of establishing the rate region for exact-repair regenerating codes for given parameters (n, k, d). Tian determined the rate region for a (4, 3, 3) code and found that it lies strictly within the functional-repair rate region. Using different methods, Sasidharan, Senthoor and Kumar prove a non-vanishing gap between the functional-repair outer bound and the exact-repa...

The problem of multilevel diversity coding with secure regeneration (MDC-SR) is considered, which includes the problems of multilevel diversity coding with regeneration (MDC-R) and secure regenerating code (SRC) as special cases. Two outer bounds are established, showing that separate coding of different messages using the respective SRCs can achieve the minimum-bandwidth-regeneration (MBR) poi...

Part I of this work answered the following fundamental question: Under and only under what (n, k, d) values does proactively choosing the helper nodes improve the storagebandwidth tradeoff of regenerating codes (RCs)? A critical component of the achievability results in Part I is a lowcomplexity helper selection solution, termed the family helper selection (FHS) scheme. In Part I, FHS was prove...