3,449 research outputs found
Lectures on Designing Screening Experiments
Designing Screening Experiments (DSE) is a class of information - theoretical
models for multiple - access channels (MAC). We discuss the combinatorial model
of DSE called a disjunct channel model. This model is the most important for
applications and closely connected with the superimposed code concept. We give
a detailed survey of lower and upper bounds on the rate of superimposed codes.
The best known constructions of superimposed codes are considered in paper. We
also discuss the development of these codes (non-adaptive pooling designs)
intended for the clone - library screening problem. We obtain lower and upper
bounds on the rate of binary codes for the combinatorial model of DSE called an
adder channel model. We also consider the concept of universal decoding for the
probabilistic DSE model called a symmetric model of DSE.Comment: 66 page
Zero-error communication over adder MAC
Adder MAC is a simple noiseless multiple-access channel (MAC), where if users
send messages , then the receiver receives with addition over . Communication over the
noiseless adder MAC has been studied for more than fifty years. There are two
models of particular interest: uniquely decodable code tuples, and -codes.
In spite of the similarities between these two models, lower bounds and upper
bounds of the optimal sum rate of uniquely decodable code tuple asymptotically
match as number of users goes to infinity, while there is a gap of factor two
between lower bounds and upper bounds of the optimal rate of -codes.
The best currently known -codes for are constructed using
random coding. In this work, we study variants of the random coding method and
related problems, in hope of achieving -codes with better rate. Our
contribution include the following. (1) We prove that changing the underlying
distribution used in random coding cannot improve the rate. (2) We determine
the rate of a list-decoding version of -codes achieved by the random
coding method. (3) We study several related problems about R\'{e}nyi entropy.Comment: An updated version of author's master thesi
Coding for Fast Content Download
We study the fundamental trade-off between storage and content download time.
We show that the download time can be significantly reduced by dividing the
content into chunks, encoding it to add redundancy and then distributing it
across multiple disks. We determine the download time for two content access
models - the fountain and fork-join models that involve simultaneous content
access, and individual access from enqueued user requests respectively. For the
fountain model we explicitly characterize the download time, while in the
fork-join model we derive the upper and lower bounds. Our results show that
coding reduces download time, through the diversity of distributing the data
across more disks, even for the total storage used.Comment: 8 pages, 6 figures, conferenc
The MDS Queue: Analysing the Latency Performance of Erasure Codes
In order to scale economically, data centers are increasingly evolving their
data storage methods from the use of simple data replication to the use of more
powerful erasure codes, which provide the same level of reliability as
replication but at a significantly lower storage cost. In particular, it is
well known that Maximum-Distance-Separable (MDS) codes, such as Reed-Solomon
codes, provide the maximum storage efficiency. While the use of codes for
providing improved reliability in archival storage systems, where the data is
less frequently accessed (or so-called "cold data"), is well understood, the
role of codes in the storage of more frequently accessed and active "hot data",
where latency is the key metric, is less clear.
In this paper, we study data storage systems based on MDS codes through the
lens of queueing theory, and term this the "MDS queue." We analytically
characterize the (average) latency performance of MDS queues, for which we
present insightful scheduling policies that form upper and lower bounds to
performance, and are observed to be quite tight. Extensive simulations are also
provided and used to validate our theoretical analysis. We also employ the
framework of the MDS queue to analyse different methods of performing so-called
degraded reads (reading of partial data) in distributed data storage
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็ญๆณขๅคงๅญฆ (University of Tsukuba)201
Probabilistic Existence Results for Separable Codes
Separable codes were defined by Cheng and Miao in 2011, motivated by
applications to the identification of pirates in a multimedia setting.
Combinatorially, -separable codes lie somewhere between
-frameproof and -frameproof codes: all -frameproof codes are
-separable, and all -separable codes are
-frameproof. Results for frameproof codes show that (when is large)
there are -ary -separable codes of length with
approximately codewords, and that no -ary
-separable codes of length can have more than approximately
codewords.
The paper provides improved probabilistic existence results for
-separable codes when . More precisely, for all and all , there exists a constant (depending only on
and ) such that there exists a -ary -separable code of
length with at least codewords for all sufficiently
large integers . This shows, in particular, that the upper bound (derived
from the bound on -frameproof codes) on the number of codewords in a
-separable code is realistic.
The results above are more surprising after examining the situation when
. Results due to Gao and Ge show that a -ary -separable
code of length can contain at most codewords, and that codes with at
least codewords exist. So optimal -separable
codes behave neither like -frameproof nor -frameproof codes.
Also, the Gao--Ge bound is strengthened to show that a -ary
-separable code of length can have at most
codewords.Comment: 16 pages. Typos corrected and minor changes since last version.
Accepted by IEEE Transactions on Information Theor
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