1,008 research outputs found
Distributed Storage Systems based on Equidistant Subspace Codes
Distributed storage systems based on equidistant constant dimension codes are
presented. These equidistant codes are based on the Pl\"{u}cker embedding,
which is essential in the repair and the reconstruction algorithms. These
systems posses several useful properties such as high failure resilience,
minimum bandwidth, low storage, simple algebraic repair and reconstruction
algorithms, good locality, and compatibility with small fields
Self-Repairing Codes for Distributed Storage - A Projective Geometric Construction
Self-Repairing Codes (SRC) are codes designed to suit the need of coding for
distributed networked storage: they not only allow stored data to be recovered
even in the presence of node failures, they also provide a repair mechanism
where as little as two live nodes can be contacted to regenerate the data of a
failed node. In this paper, we propose a new instance of self-repairing codes,
based on constructions of spreads coming from projective geometry. We study
some of their properties to demonstrate the suitability of these codes for
distributed networked storage.Comment: 5 pages, 2 figure
Codes for Updating Linear Functions over Small Fields
We consider a point-to-point communication scenario where the receiver
maintains a specific linear function of a message vector over a finite field.
When the value of the message vector undergoes a sparse update, the transmitter
broadcasts a coded version of the modified message while the receiver uses this
codeword and the current value of the linear function to update its contents.
It is assumed that the transmitter has access to the modified message but is
unaware of the exact difference vector between the original and modified
messages. Under the assumption that the difference vector is sparse and that
its Hamming weight is at the most a known constant, the objective is to design
a linear code with as small a codelength as possible that allows successful
update of the linear function at the receiver. This problem is motivated by
applications to distributed data storage systems. Recently, Prakash and Medard
derived a lower bound on the codelength, which is independent of the size of
the underlying finite field, and provided constructions that achieve this bound
if the size of the finite field is sufficiently large. However, this
requirement on the field size can be prohibitive for even moderate values of
the system parameters. In this paper, we provide a field-size aware analysis of
the function update problem, including a tighter lower bound on the codelength,
and design codes that trade-off the codelength for a smaller field size
requirement. We first characterize the family of function update problems where
linear coding can provide reduction in codelength compared to a naive
transmission scheme. We then provide field-size dependent bounds on the optimal
codelength, and construct coding schemes when the receiver maintains linear
functions of striped message vector. Finally, we show that every function
update problem is equivalent to a generalized index coding problem.Comment: Keywords: distributed storage systems, function update problem, index
coding, side informatio
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