20,932 research outputs found
Generalized Gray Codes for Local Rank Modulation
We consider the local rank-modulation scheme in which a sliding window going
over a sequence of real-valued variables induces a sequence of permutations.
Local rank-modulation is a generalization of the rank-modulation scheme, which
has been recently suggested as a way of storing information in flash memory. We
study Gray codes for the local rank-modulation scheme in order to simulate
conventional multi-level flash cells while retaining the benefits of rank
modulation. Unlike the limited scope of previous works, we consider code
constructions for the entire range of parameters including the code length,
sliding window size, and overlap between adjacent windows. We show our
constructed codes have asymptotically-optimal rate. We also provide efficient
encoding, decoding, and next-state algorithms.Comment: 7 pages, 1 figure, shorter version was submitted to ISIT 201
A domain decomposition strategy to efficiently solve structures containing repeated patterns
This paper presents a strategy for the computation of structures with
repeated patterns based on domain decomposition and block Krylov solvers. It
can be seen as a special variant of the FETI method. We propose using the
presence of repeated domains in the problem to compute the solution by
minimizing the interface error on several directions simultaneously. The method
not only drastically decreases the size of the problems to solve but also
accelerates the convergence of interface problem for nearly no additional
computational cost and minimizes expensive memory accesses. The numerical
performances are illustrated on some thermal and elastic academic problems
Enhanced Recursive Reed-Muller Erasure Decoding
Recent work have shown that Reed-Muller (RM) codes achieve the erasure
channel capacity. However, this performance is obtained with maximum-likelihood
decoding which can be costly for practical applications. In this paper, we
propose an encoding/decoding scheme for Reed-Muller codes on the packet erasure
channel based on Plotkin construction. We present several improvements over the
generic decoding. They allow, for a light cost, to compete with
maximum-likelihood decoding performance, especially on high-rate codes, while
significantly outperforming it in terms of speed
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