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Locally repairable codes (LRC) for distributed storage allow two approaches to locally repair multiple failed nodes: 1) parallel approach, by which each newcomer access a set of live nodes $(r$ is the repair locality$)$ to download data and recover the lost packet; and 2) sequential approach, by which the newcomers are properly ordered and each newcomer access a set of other nodes, which can be...
We introduce a new family of erasure codes, called group decodable code (GDC), for distributed storage system. Given a set of design parameters {α, β, k, t}, where k is the number of information symbols, each codeword of an (α, β, k, t)- group decodable code is a t-tuple of strings, called buckets, such that each bucket is a string of β symbols that is a codeword of a [β, α] MDS code (which is encoded...
We consider the complexities of repair algorithms for locally repairable codes and propose a class of codes that repair single node failures using addition operations only, or codes with addition based repair. We construct two families of codes with addition based repair. The first family attains distance one less than the Singleton-like upper bound, while the second family attains the Singleton-like...
Linear erasure codes with local repairability are desirable for distributed data storage systems. An [n,k,d] linear code having all-symbol (r,δ)-locality, denoted as (r,δ)_a, is considered optimal if it has the actual highest minimum distance of any code of the given parameters n,k,r and δ. A minimum distance bound is given in . The existing results on the existence and the construction of optimal...
In this paper, a class of quasi-orthogonal space-time block codes (Q-STBC) is proposed for systems with 2 antennas and 3 time slots, where the orthogonal Alamouti code can not be applied due to the “odd symbol” problem inherited in the 3GPP frame structure. The proposed codes can achieve rate one and full diversity with lower complexity maximum likelihood detection. The design takes into consideration...
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