43 research outputs found
Self-repairing Homomorphic Codes for Distributed Storage Systems
Erasure codes provide a storage efficient alternative to replication based
redundancy in (networked) storage systems. They however entail high
communication overhead for maintenance, when some of the encoded fragments are
lost and need to be replenished. Such overheads arise from the fundamental need
to recreate (or keep separately) first a copy of the whole object before any
individual encoded fragment can be generated and replenished. There has been
recently intense interest to explore alternatives, most prominent ones being
regenerating codes (RGC) and hierarchical codes (HC). We propose as an
alternative a new family of codes to improve the maintenance process, which we
call self-repairing codes (SRC), with the following salient features: (a)
encoded fragments can be repaired directly from other subsets of encoded
fragments without having to reconstruct first the original data, ensuring that
(b) a fragment is repaired from a fixed number of encoded fragments, the number
depending only on how many encoded blocks are missing and independent of which
specific blocks are missing. These properties allow for not only low
communication overhead to recreate a missing fragment, but also independent
reconstruction of different missing fragments in parallel, possibly in
different parts of the network. We analyze the static resilience of SRCs with
respect to traditional erasure codes, and observe that SRCs incur marginally
larger storage overhead in order to achieve the aforementioned properties. The
salient SRC properties naturally translate to low communication overheads for
reconstruction of lost fragments, and allow reconstruction with lower latency
by facilitating repairs in parallel. These desirable properties make
self-repairing codes a good and practical candidate for networked distributed
storage systems
Families of unitary matrices achieving full diversity
This paper presents an algebraic construction of families of unitary matrices
that achieve full diversity. They are obtained as subsets of cyclic division
algebras.Comment: To appear in the proceedings of the 2005 IEEE International Symposium
on Information Theory, Adelaide, Australia, September 4-9, 200
Codes over Matrix Rings for Space-Time Coded Modulations
It is known that, for transmission over quasi-static MIMO fading channels
with n transmit antennas, diversity can be obtained by using an inner fully
diverse space-time block code while coding gain, derived from the determinant
criterion, comes from an appropriate outer code. When the inner code has a
cyclic algebra structure over a number field, as for perfect space-time codes,
an outer code can be designed via coset coding. More precisely, we take the
quotient of the algebra by a two-sided ideal which leads to a finite alphabet
for the outer code, with a cyclic algebra structure over a finite field or a
finite ring. We show that the determinant criterion induces various metrics on
the outer code, such as the Hamming and Bachoc distances. When n=2,
partitioning the 2x2 Golden code by using an ideal above the prime 2 leads to
consider codes over either M2(F_2) or M2(F_2[i]), both being non-commutative
alphabets. Matrix rings of higher dimension, suitable for 3x3 and 4x4 perfect
codes, give rise to more complex examples
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