32 research outputs found
On Critical Relative Distance of DNA Codes for Additive Stem Similarity
We consider DNA codes based on the nearest-neighbor (stem) similarity model
which adequately reflects the "hybridization potential" of two DNA sequences.
Our aim is to present a survey of bounds on the rate of DNA codes with respect
to a thermodynamically motivated similarity measure called an additive stem
similarity. These results yield a method to analyze and compare known samples
of the nearest neighbor "thermodynamic weights" associated to stacked pairs
that occurred in DNA secondary structures.Comment: 5 or 6 pages (compiler-dependable), 0 figures, submitted to 2010 IEEE
International Symposium on Information Theory (ISIT 2010), uses IEEEtran.cl
Random Coding Bounds for DNA Codes Based on Fibonacci Ensembles of DNA Sequences
We consider DNA codes based on the concept of a weighted 2-stem similarity measure which reflects the ”hybridization potential” of two DNA sequences. A random coding bound on the rate of DNA codes with respect to a thermodynamic motivated similarity measure is proved. Ensembles of DNA strands whose sequence composition is restricted in a manner similar to the restrictions in binary Fibonacci sequences are introduced to obtain the bound
Noise-Resilient Group Testing: Limitations and Constructions
We study combinatorial group testing schemes for learning -sparse Boolean
vectors using highly unreliable disjunctive measurements. We consider an
adversarial noise model that only limits the number of false observations, and
show that any noise-resilient scheme in this model can only approximately
reconstruct the sparse vector. On the positive side, we take this barrier to
our advantage and show that approximate reconstruction (within a satisfactory
degree of approximation) allows us to break the information theoretic lower
bound of that is known for exact reconstruction of
-sparse vectors of length via non-adaptive measurements, by a
multiplicative factor .
Specifically, we give simple randomized constructions of non-adaptive
measurement schemes, with measurements, that allow efficient
reconstruction of -sparse vectors up to false positives even in the
presence of false positives and false negatives within the
measurement outcomes, for any constant . We show that, information
theoretically, none of these parameters can be substantially improved without
dramatically affecting the others. Furthermore, we obtain several explicit
constructions, in particular one matching the randomized trade-off but using measurements. We also obtain explicit constructions
that allow fast reconstruction in time \poly(m), which would be sublinear in
for sufficiently sparse vectors. The main tool used in our construction is
the list-decoding view of randomness condensers and extractors.Comment: Full version. A preliminary summary of this work appears (under the
same title) in proceedings of the 17th International Symposium on
Fundamentals of Computation Theory (FCT 2009
Group testing with Random Pools: Phase Transitions and Optimal Strategy
The problem of Group Testing is to identify defective items out of a set of
objects by means of pool queries of the form "Does the pool contain at least a
defective?". The aim is of course to perform detection with the fewest possible
queries, a problem which has relevant practical applications in different
fields including molecular biology and computer science. Here we study GT in
the probabilistic setting focusing on the regime of small defective probability
and large number of objects, and . We construct and
analyze one-stage algorithms for which we establish the occurrence of a
non-detection/detection phase transition resulting in a sharp threshold, , for the number of tests. By optimizing the pool design we construct
algorithms whose detection threshold follows the optimal scaling . Then we consider two-stages algorithms and analyze their
performance for different choices of the first stage pools. In particular, via
a proper random choice of the pools, we construct algorithms which attain the
optimal value (previously determined in Ref. [16]) for the mean number of tests
required for complete detection. We finally discuss the optimal pool design in
the case of finite
Improved Adaptive Group Testing Algorithms with Applications to Multiple Access Channels and Dead Sensor Diagnosis
We study group-testing algorithms for resolving broadcast conflicts on a
multiple access channel (MAC) and for identifying the dead sensors in a mobile
ad hoc wireless network. In group-testing algorithms, we are asked to identify
all the defective items in a set of items when we can test arbitrary subsets of
items. In the standard group-testing problem, the result of a test is
binary--the tested subset either contains defective items or not. In the more
generalized versions we study in this paper, the result of each test is
non-binary. For example, it may indicate whether the number of defective items
contained in the tested subset is zero, one, or at least two. We give adaptive
algorithms that are provably more efficient than previous group testing
algorithms. We also show how our algorithms can be applied to solve conflict
resolution on a MAC and dead sensor diagnosis. Dead sensor diagnosis poses an
interesting challenge compared to MAC resolution, because dead sensors are not
locally detectable, nor are they themselves active participants.Comment: Expanded version of a paper appearing in ACM Symposium on Parallelism
in Algorithms and Architectures (SPAA), and preliminary version of paper
appearing in Journal of Combinatorial Optimizatio
Symmetric-key Corruption Detection : When XOR-MACs Meet Combinatorial Group Testing
We study a class of MACs, which we call corruption detectable MAC, that is able to not only check the integrity of the whole message, but also detect a part of the message that is corrupted.
It can be seen as an application of the classical Combinatorial Group Testing (CGT) to message authentication.
However, previous work on this application has inherent limitation in communication.
We present a novel approach to combine CGT and a class of linear MACs (XOR-MAC) that enables to break this limit. Our proposal, XOR-GTM, has a significantly smaller communication cost than any of the previous ones, keeping the same corruption detection capability. Our numerical examples for storage application show a reduction of communication by a factor of around 15 to 70 compared with previous schemes.
XOR-GTM is parallelizable and is as efficient as standard MACs.
We prove that XOR-GTM is provably secure under the standard pseudorandomness assumptions