60,885 research outputs found
Update-Efficient Regenerating Codes with Minimum Per-Node Storage
Regenerating codes provide an efficient way to recover data at failed nodes
in distributed storage systems. It has been shown that regenerating codes can
be designed to minimize the per-node storage (called MSR) or minimize the
communication overhead for regeneration (called MBR). In this work, we propose
a new encoding scheme for [n,d] error- correcting MSR codes that generalizes
our earlier work on error-correcting regenerating codes. We show that by
choosing a suitable diagonal matrix, any generator matrix of the [n,{\alpha}]
Reed-Solomon (RS) code can be integrated into the encoding matrix. Hence, MSR
codes with the least update complexity can be found. An efficient decoding
scheme is also proposed that utilizes the [n,{\alpha}] RS code to perform data
reconstruction. The proposed decoding scheme has better error correction
capability and incurs the least number of node accesses when errors are
present.Comment: Submitted to IEEE ISIT 201
Update-Efficiency and Local Repairability Limits for Capacity Approaching Codes
Motivated by distributed storage applications, we investigate the degree to
which capacity achieving encodings can be efficiently updated when a single
information bit changes, and the degree to which such encodings can be
efficiently (i.e., locally) repaired when single encoded bit is lost.
Specifically, we first develop conditions under which optimum
error-correction and update-efficiency are possible, and establish that the
number of encoded bits that must change in response to a change in a single
information bit must scale logarithmically in the block-length of the code if
we are to achieve any nontrivial rate with vanishing probability of error over
the binary erasure or binary symmetric channels. Moreover, we show there exist
capacity-achieving codes with this scaling.
With respect to local repairability, we develop tight upper and lower bounds
on the number of remaining encoded bits that are needed to recover a single
lost bit of the encoding. In particular, we show that if the code-rate is
less than the capacity, then for optimal codes, the maximum number
of codeword symbols required to recover one lost symbol must scale as
.
Several variations on---and extensions of---these results are also developed.Comment: Accepted to appear in JSA
Efficient Decoding of Topological Color Codes
Color codes are a class of topological quantum codes with a high error
threshold and large set of transversal encoded gates, and are thus suitable for
fault tolerant quantum computation in two-dimensional architectures. Recently,
computationally efficient decoders for the color codes were proposed. We
describe an alternate efficient iterative decoder for topological color codes,
and apply it to the color code on hexagonal lattice embedded on a torus. In
numerical simulations, we find an error threshold of 7.8% for independent
dephasing and spin flip errors.Comment: 7 pages, LaTe
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