41,524 research outputs found
Time-Space Constrained Codes for Phase-Change Memories
Phase-change memory (PCM) is a promising non-volatile solid-state memory
technology. A PCM cell stores data by using its amorphous and crystalline
states. The cell changes between these two states using high temperature.
However, since the cells are sensitive to high temperature, it is important,
when programming cells, to balance the heat both in time and space.
In this paper, we study the time-space constraint for PCM, which was
originally proposed by Jiang et al. A code is called an
\emph{-constrained code} if for any consecutive
rewrites and for any segment of contiguous cells, the total rewrite
cost of the cells over those rewrites is at most . Here,
the cells are binary and the rewrite cost is defined to be the Hamming distance
between the current and next memory states. First, we show a general upper
bound on the achievable rate of these codes which extends the results of Jiang
et al. Then, we generalize their construction for -constrained codes and show another construction for -constrained codes. Finally, we show that these two
constructions can be used to construct codes for all values of ,
, and
Trajectory Codes for Flash Memory
Flash memory is well-known for its inherent asymmetry: the flash-cell charge
levels are easy to increase but are hard to decrease. In a general rewriting
model, the stored data changes its value with certain patterns. The patterns of
data updates are determined by the data structure and the application, and are
independent of the constraints imposed by the storage medium. Thus, an
appropriate coding scheme is needed so that the data changes can be updated and
stored efficiently under the storage-medium's constraints.
In this paper, we define the general rewriting problem using a graph model.
It extends many known rewriting models such as floating codes, WOM codes,
buffer codes, etc. We present a new rewriting scheme for flash memories, called
the trajectory code, for rewriting the stored data as many times as possible
without block erasures. We prove that the trajectory code is asymptotically
optimal in a wide range of scenarios.
We also present randomized rewriting codes optimized for expected performance
(given arbitrary rewriting sequences). Our rewriting codes are shown to be
asymptotically optimal.Comment: Submitted to IEEE Trans. on Inform. Theor
Rewriting Codes for Joint Information Storage in Flash Memories
Memories whose storage cells transit irreversibly between
states have been common since the start of the data storage
technology. In recent years, flash memories have become a very
important family of such memories. A flash memory cell has q
states—state 0.1.....q-1 - and can only transit from a lower
state to a higher state before the expensive erasure operation takes
place. We study rewriting codes that enable the data stored in a
group of cells to be rewritten by only shifting the cells to higher
states. Since the considered state transitions are irreversible, the
number of rewrites is bounded. Our objective is to maximize the
number of times the data can be rewritten. We focus on the joint
storage of data in flash memories, and study two rewriting codes
for two different scenarios. The first code, called floating code, is for
the joint storage of multiple variables, where every rewrite changes
one variable. The second code, called buffer code, is for remembering
the most recent data in a data stream. Many of the codes
presented here are either optimal or asymptotically optimal. We
also present bounds to the performance of general codes. The results
show that rewriting codes can integrate a flash memory’s
rewriting capabilities for different variables to a high degree
Systematic Error-Correcting Codes for Rank Modulation
The rank-modulation scheme has been recently proposed for efficiently storing
data in nonvolatile memories. Error-correcting codes are essential for rank
modulation, however, existing results have been limited. In this work we
explore a new approach, \emph{systematic error-correcting codes for rank
modulation}. Systematic codes have the benefits of enabling efficient
information retrieval and potentially supporting more efficient encoding and
decoding procedures. We study systematic codes for rank modulation under
Kendall's -metric as well as under the -metric.
In Kendall's -metric we present -systematic codes for
correcting one error, which have optimal rates, unless systematic perfect codes
exist. We also study the design of multi-error-correcting codes, and provide
two explicit constructions, one resulting in systematic codes
with redundancy at most . We use non-constructive arguments to show the
existence of -systematic codes for general parameters. Furthermore,
we prove that for rank modulation, systematic codes achieve the same capacity
as general error-correcting codes.
Finally, in the -metric we construct two systematic
multi-error-correcting codes, the first for the case of , and the
second for . In the latter case, the codes have the same
asymptotic rate as the best codes currently known in this metric
Quantum noise, entanglement and chaos in the quantum field theory of mind/brain states
We review the dissipative quantum model of brain and present recent
developments related with the r\^ole of entanglement, quantum noise and chaos
in the model.Comment: 15 page
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