216 research outputs found
The benefit of a 1-bit jump-start, and the necessity of stochastic encoding, in jamming channels
We consider the problem of communicating a message in the presence of a
malicious jamming adversary (Calvin), who can erase an arbitrary set of up to
bits, out of transmitted bits . The capacity of such
a channel when Calvin is exactly causal, i.e. Calvin's decision of whether or
not to erase bit depends on his observations was
recently characterized to be . In this work we show two (perhaps)
surprising phenomena. Firstly, we demonstrate via a novel code construction
that if Calvin is delayed by even a single bit, i.e. Calvin's decision of
whether or not to erase bit depends only on (and
is independent of the "current bit" ) then the capacity increases to
when the encoder is allowed to be stochastic. Secondly, we show via a novel
jamming strategy for Calvin that, in the single-bit-delay setting, if the
encoding is deterministic (i.e. the transmitted codeword is a deterministic
function of the message ) then no rate asymptotically larger than is
possible with vanishing probability of error, hence stochastic encoding (using
private randomness at the encoder) is essential to achieve the capacity of
against a one-bit-delayed Calvin.Comment: 21 pages, 4 figures, extended draft of submission to ISIT 201
Asymmetric Error Correction and Flash-Memory Rewriting using Polar Codes
We propose efficient coding schemes for two communication settings: 1.
asymmetric channels, and 2. channels with an informed encoder. These settings
are important in non-volatile memories, as well as optical and broadcast
communication. The schemes are based on non-linear polar codes, and they build
on and improve recent work on these settings. In asymmetric channels, we tackle
the exponential storage requirement of previously known schemes, that resulted
from the use of large Boolean functions. We propose an improved scheme, that
achieves the capacity of asymmetric channels with polynomial computational
complexity and storage requirement.
The proposed non-linear scheme is then generalized to the setting of channel
coding with an informed encoder, using a multicoding technique. We consider
specific instances of the scheme for flash memories, that incorporate
error-correction capabilities together with rewriting. Since the considered
codes are non-linear, they eliminate the requirement of previously known
schemes (called polar write-once-memory codes) for shared randomness between
the encoder and the decoder. Finally, we mention that the multicoding scheme is
also useful for broadcast communication in Marton's region, improving upon
previous schemes for this setting.Comment: Submitted to IEEE Transactions on Information Theory. Partially
presented at ISIT 201
Quantum channels and memory effects
Any physical process can be represented as a quantum channel mapping an
initial state to a final state. Hence it can be characterized from the point of
view of communication theory, i.e., in terms of its ability to transfer
information. Quantum information provides a theoretical framework and the
proper mathematical tools to accomplish this. In this context the notion of
codes and communication capacities have been introduced by generalizing them
from the classical Shannon theory of information transmission and error
correction. The underlying assumption of this approach is to consider the
channel not as acting on a single system, but on sequences of systems, which,
when properly initialized allow one to overcome the noisy effects induced by
the physical process under consideration. While most of the work produced so
far has been focused on the case in which a given channel transformation acts
identically and independently on the various elements of the sequence
(memoryless configuration in jargon), correlated error models appear to be a
more realistic way to approach the problem. A slightly different, yet
conceptually related, notion of correlated errors applies to a single quantum
system which evolves continuously in time under the influence of an external
disturbance which acts on it in a non-Markovian fashion. This leads to the
study of memory effects in quantum channels: a fertile ground where interesting
novel phenomena emerge at the intersection of quantum information theory and
other branches of physics. A survey is taken of the field of quantum channels
theory while also embracing these specific and complex settings.Comment: Review article, 61 pages, 26 figures; 400 references. Final version
of the manuscript, typos correcte
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