9,801 research outputs found
Codes for Asymmetric Limited-Magnitude Errors With Application to Multilevel Flash Memories
Several physical effects that limit the reliability and performance of multilevel flash memories induce errors that have low magnitudes and are dominantly asymmetric. This paper studies block codes for asymmetric limited-magnitude errors over q-ary channels. We propose code constructions and bounds for such channels when the number of errors is bounded by t and the error magnitudes are bounded by â. The constructions utilize known codes for symmetric errors, over small alphabets, to protect large-alphabet symbols from asymmetric limited-magnitude errors. The encoding and decoding of these codes are performed over the small alphabet whose size depends only on the maximum error magnitude and is independent of the alphabet size of the outer code. Moreover, the size of the codes is shown to exceed the sizes of known codes (for related error models), and asymptotic rate-optimality results are proved. Extensions of the construction are proposed to accommodate variations on the error model and to include systematic codes as a benefit to practical implementation
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On the Computational Power of Radio Channels
Radio networks can be a challenging platform for which to develop distributed algorithms, because the network nodes must contend for a shared channel. In some cases, though, the shared medium is an advantage rather than a disadvantage: for example, many radio network algorithms cleverly use the shared channel to approximate the degree of a node, or estimate the contention. In this paper we ask how far the inherent power of a shared radio channel goes, and whether it can efficiently compute "classicaly hard" functions such as Majority, Approximate Sum, and Parity.
Using techniques from circuit complexity, we show that in many cases, the answer is "no". We show that simple radio channels, such as the beeping model or the channel with collision-detection, can be approximated by a low-degree polynomial, which makes them subject to known lower bounds on functions such as Parity and Majority; we obtain round lower bounds of the form Omega(n^{delta}) on these functions, for delta in (0,1). Next, we use the technique of random restrictions, used to prove AC^0 lower bounds, to prove a tight lower bound of Omega(1/epsilon^2) on computing a (1 +/- epsilon)-approximation to the sum of the nodes\u27 inputs. Our techniques are general, and apply to many types of radio channels studied in the literature
Improved Pseudorandom Generators from Pseudorandom Multi-Switching Lemmas
We give the best known pseudorandom generators for two touchstone classes in
unconditional derandomization: an -PRG for the class of size-
depth- circuits with seed length , and an -PRG for the class of -sparse
polynomials with seed length . These results bring the state of the art for
unconditional derandomization of these classes into sharp alignment with the
state of the art for computational hardness for all parameter settings:
improving on the seed lengths of either PRG would require breakthrough progress
on longstanding and notorious circuit lower bounds.
The key enabling ingredient in our approach is a new \emph{pseudorandom
multi-switching lemma}. We derandomize recently-developed
\emph{multi}-switching lemmas, which are powerful generalizations of
H{\aa}stad's switching lemma that deal with \emph{families} of depth-two
circuits. Our pseudorandom multi-switching lemma---a randomness-efficient
algorithm for sampling restrictions that simultaneously simplify all circuits
in a family---achieves the parameters obtained by the (full randomness)
multi-switching lemmas of Impagliazzo, Matthews, and Paturi [IMP12] and
H{\aa}stad [H{\aa}s14]. This optimality of our derandomization translates into
the optimality (given current circuit lower bounds) of our PRGs for
and sparse polynomials
A Multi-Core Solver for Parity Games
We describe a parallel algorithm for solving parity games,\ud
with applications in, e.g., modal mu-calculus model\ud
checking with arbitrary alternations, and (branching) bisimulation\ud
checking. The algorithm is based on Jurdzinski's Small Progress\ud
Measures. Actually, this is a class of algorithms, depending on\ud
a selection heuristics.\ud
\ud
Our algorithm operates lock-free, and mostly wait-free (except for\ud
infrequent termination detection), and thus allows maximum\ud
parallelism. Additionally, we conserve memory by avoiding storage\ud
of predecessor edges for the parity graph through strictly\ud
forward-looking heuristics.\ud
\ud
We evaluate our multi-core implementation's behaviour on parity games\ud
obtained from mu-calculus model checking problems for a set of\ud
communication protocols, randomly generated problem instances, and\ud
parametric problem instances from the literature.\ud
\u
Closed-Form Bayesian Inferences for the Logit Model via Polynomial Expansions
Articles in Marketing and choice literatures have demonstrated the need for
incorporating person-level heterogeneity into behavioral models (e.g., logit
models for multiple binary outcomes as studied here). However, the logit
likelihood extended with a population distribution of heterogeneity doesn't
yield closed-form inferences, and therefore numerical integration techniques
are relied upon (e.g., MCMC methods).
We present here an alternative, closed-form Bayesian inferences for the logit
model, which we obtain by approximating the logit likelihood via a polynomial
expansion, and then positing a distribution of heterogeneity from a flexible
family that is now conjugate and integrable. For problems where the response
coefficients are independent, choosing the Gamma distribution leads to rapidly
convergent closed-form expansions; if there are correlations among the
coefficients one can still obtain rapidly convergent closed-form expansions by
positing a distribution of heterogeneity from a Multivariate Gamma
distribution. The solution then comes from the moment generating function of
the Multivariate Gamma distribution or in general from the multivariate
heterogeneity distribution assumed.
Closed-form Bayesian inferences, derivatives (useful for elasticity
calculations), population distribution parameter estimates (useful for
summarization) and starting values (useful for complicated algorithms) are
hence directly available. Two simulation studies demonstrate the efficacy of
our approach.Comment: 30 pages, 2 figures, corrected some typos. Appears in Quantitative
Marketing and Economics vol 4 (2006), no. 2, 173--20
Efficient quantum algorithms for simulating sparse Hamiltonians
We present an efficient quantum algorithm for simulating the evolution of a
sparse Hamiltonian H for a given time t in terms of a procedure for computing
the matrix entries of H. In particular, when H acts on n qubits, has at most a
constant number of nonzero entries in each row/column, and |H| is bounded by a
constant, we may select any positive integer such that the simulation
requires O((\log^*n)t^{1+1/2k}) accesses to matrix entries of H. We show that
the temporal scaling cannot be significantly improved beyond this, because
sublinear time scaling is not possible.Comment: 9 pages, 2 figures, substantial revision
DNF Sparsification and a Faster Deterministic Counting Algorithm
Given a DNF formula on n variables, the two natural size measures are the
number of terms or size s(f), and the maximum width of a term w(f). It is
folklore that short DNF formulas can be made narrow. We prove a converse,
showing that narrow formulas can be sparsified. More precisely, any width w DNF
irrespective of its size can be -approximated by a width DNF with
at most terms.
We combine our sparsification result with the work of Luby and Velikovic to
give a faster deterministic algorithm for approximately counting the number of
satisfying solutions to a DNF. Given a formula on n variables with poly(n)
terms, we give a deterministic time algorithm
that computes an additive approximation to the fraction of
satisfying assignments of f for \epsilon = 1/\poly(\log n). The previous best
result due to Luby and Velickovic from nearly two decades ago had a run-time of
.Comment: To appear in the IEEE Conference on Computational Complexity, 201
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