3,602 research outputs found
On Coding Efficiency for Flash Memories
Recently, flash memories have become a competitive solution for mass storage.
The flash memories have rather different properties compared with the rotary
hard drives. That is, the writing of flash memories is constrained, and flash
memories can endure only limited numbers of erases. Therefore, the design goals
for the flash memory systems are quite different from these for other memory
systems. In this paper, we consider the problem of coding efficiency. We define
the "coding-efficiency" as the amount of information that one flash memory cell
can be used to record per cost. Because each flash memory cell can endure a
roughly fixed number of erases, the cost of data recording can be well-defined.
We define "payload" as the amount of information that one flash memory cell can
represent at a particular moment. By using information-theoretic arguments, we
prove a coding theorem for achievable coding rates. We prove an upper and lower
bound for coding efficiency. We show in this paper that there exists a
fundamental trade-off between "payload" and "coding efficiency". The results in
this paper may provide useful insights on the design of future flash memory
systems.Comment: accepted for publication in the Proceeding of the 35th IEEE Sarnoff
Symposium, Newark, New Jersey, May 21-22, 201
Energy Requirements for Quantum Data Compression and 1-1 Coding
By looking at quantum data compression in the second quantisation, we present
a new model for the efficient generation and use of variable length codes. In
this picture lossless data compression can be seen as the {\em minimum energy}
required to faithfully represent or transmit classical information contained
within a quantum state.
In order to represent information we create quanta in some predefined modes
(i.e. frequencies) prepared in one of two possible internal states (the
information carrying degrees of freedom). Data compression is now seen as the
selective annihilation of these quanta, the energy of whom is effectively
dissipated into the environment. As any increase in the energy of the
environment is intricately linked to any information loss and is subject to
Landauer's erasure principle, we use this principle to distinguish lossless and
lossy schemes and to suggest bounds on the efficiency of our lossless
compression protocol.
In line with the work of Bostr\"{o}m and Felbinger \cite{bostroem}, we also
show that when using variable length codes the classical notions of prefix or
uniquely decipherable codes are unnecessarily restrictive given the structure
of quantum mechanics and that a 1-1 mapping is sufficient. In the absence of
this restraint we translate existing classical results on 1-1 coding to the
quantum domain to derive a new upper bound on the compression of quantum
information. Finally we present a simple quantum circuit to implement our
scheme.Comment: 10 pages, 5 figure
Quantum Information Complexity and Amortized Communication
We define a new notion of information cost for quantum protocols, and a
corresponding notion of quantum information complexity for bipartite quantum
channels, and then investigate the properties of such quantities. These are the
fully quantum generalizations of the analogous quantities for bipartite
classical functions that have found many applications recently, in particular
for proving communication complexity lower bounds. Our definition is strongly
tied to the quantum state redistribution task.
Previous attempts have been made to define such a quantity for quantum
protocols, with particular applications in mind; our notion differs from these
in many respects. First, it directly provides a lower bound on the quantum
communication cost, independent of the number of rounds of the underlying
protocol. Secondly, we provide an operational interpretation for quantum
information complexity: we show that it is exactly equal to the amortized
quantum communication complexity of a bipartite channel on a given state. This
generalizes a result of Braverman and Rao to quantum protocols, and even
strengthens the classical result in a bounded round scenario. Also, this
provides an analogue of the Schumacher source compression theorem for
interactive quantum protocols, and answers a question raised by Braverman.
We also discuss some potential applications to quantum communication
complexity lower bounds by specializing our definition for classical functions
and inputs. Building on work of Jain, Radhakrishnan and Sen, we provide new
evidence suggesting that the bounded round quantum communication complexity of
the disjointness function is \Omega (n/M + M), for M-message protocols. This
would match the best known upper bound.Comment: v1, 38 pages, 1 figur
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