3,062 research outputs found
Coding for Racetrack Memories
Racetrack memory is a new technology which utilizes magnetic domains along a
nanoscopic wire in order to obtain extremely high storage density. In racetrack
memory, each magnetic domain can store a single bit of information, which can
be sensed by a reading port (head). The memory has a tape-like structure which
supports a shift operation that moves the domains to be read sequentially by
the head. In order to increase the memory's speed, prior work studied how to
minimize the latency of the shift operation, while the no less important
reliability of this operation has received only a little attention.
In this work we design codes which combat shift errors in racetrack memory,
called position errors. Namely, shifting the domains is not an error-free
operation and the domains may be over-shifted or are not shifted, which can be
modeled as deletions and sticky insertions. While it is possible to use
conventional deletion and insertion-correcting codes, we tackle this problem
with the special structure of racetrack memory, where the domains can be read
by multiple heads. Each head outputs a noisy version of the stored data and the
multiple outputs are combined in order to reconstruct the data. Under this
paradigm, we will show that it is possible to correct, with at most a single
bit of redundancy, deletions with heads if the heads are
well-separated. Similar results are provided for burst of deletions, sticky
insertions and combinations of both deletions and sticky insertions
The Wavelet Trie: Maintaining an Indexed Sequence of Strings in Compressed Space
An indexed sequence of strings is a data structure for storing a string
sequence that supports random access, searching, range counting and analytics
operations, both for exact matches and prefix search. String sequences lie at
the core of column-oriented databases, log processing, and other storage and
query tasks. In these applications each string can appear several times and the
order of the strings in the sequence is relevant. The prefix structure of the
strings is relevant as well: common prefixes are sought in strings to extract
interesting features from the sequence. Moreover, space-efficiency is highly
desirable as it translates directly into higher performance, since more data
can fit in fast memory.
We introduce and study the problem of compressed indexed sequence of strings,
representing indexed sequences of strings in nearly-optimal compressed space,
both in the static and dynamic settings, while preserving provably good
performance for the supported operations.
We present a new data structure for this problem, the Wavelet Trie, which
combines the classical Patricia Trie with the Wavelet Tree, a succinct data
structure for storing a compressed sequence. The resulting Wavelet Trie
smoothly adapts to a sequence of strings that changes over time. It improves on
the state-of-the-art compressed data structures by supporting a dynamic
alphabet (i.e. the set of distinct strings) and prefix queries, both crucial
requirements in the aforementioned applications, and on traditional indexes by
reducing space occupancy to close to the entropy of the sequence
Numerically erasure-robust frames
Given a channel with additive noise and adversarial erasures, the task is to
design a frame that allows for stable signal reconstruction from transmitted
frame coefficients. To meet these specifications, we introduce numerically
erasure-robust frames. We first consider a variety of constructions, including
random frames, equiangular tight frames and group frames. Later, we show that
arbitrarily large erasure rates necessarily induce numerical instability in
signal reconstruction. We conclude with a few observations, including some
implications for maximal equiangular tight frames and sparse frames.Comment: 15 page
Phase retrieval with polarization
In many areas of imaging science, it is difficult to measure the phase of
linear measurements. As such, one often wishes to reconstruct a signal from
intensity measurements, that is, perform phase retrieval. In this paper, we
provide a novel measurement design which is inspired by interferometry and
exploits certain properties of expander graphs. We also give an efficient phase
retrieval procedure, and use recent results in spectral graph theory to produce
a stable performance guarantee which rivals the guarantee for PhaseLift in
[Candes et al. 2011]. We use numerical simulations to illustrate the
performance of our phase retrieval procedure, and we compare reconstruction
error and runtime with a common alternating-projections-type procedure
On the Error Resilience of Ordered Binary Decision Diagrams
Ordered Binary Decision Diagrams (OBDDs) are a data structure that is used in
an increasing number of fields of Computer Science (e.g., logic synthesis,
program verification, data mining, bioinformatics, and data protection) for
representing and manipulating discrete structures and Boolean functions. The
purpose of this paper is to study the error resilience of OBDDs and to design a
resilient version of this data structure, i.e., a self-repairing OBDD. In
particular, we describe some strategies that make reduced ordered OBDDs
resilient to errors in the indexes, that are associated to the input variables,
or in the pointers (i.e., OBDD edges) of the nodes. These strategies exploit
the inherent redundancy of the data structure, as well as the redundancy
introduced by its efficient implementations. The solutions we propose allow the
exact restoring of the original OBDD and are suitable to be applied to
classical software packages for the manipulation of OBDDs currently in use.
Another result of the paper is the definition of a new canonical OBDD model,
called {\em Index-resilient Reduced OBDD}, which guarantees that a node with a
faulty index has a reconstruction cost , where is the number of nodes
with corrupted index
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