22 research outputs found
Upper Bounds on the Capacity of Binary Channels with Causal Adversaries
In this work we consider the communication of information in the presence of
a causal adversarial jammer. In the setting under study, a sender wishes to
communicate a message to a receiver by transmitting a codeword
bit-by-bit over a communication channel. The sender and the receiver do not
share common randomness. The adversarial jammer can view the transmitted bits
one at a time, and can change up to a -fraction of them. However, the
decisions of the jammer must be made in a causal manner. Namely, for each bit
the jammer's decision on whether to corrupt it or not must depend only on
for . This is in contrast to the "classical" adversarial
jamming situations in which the jammer has no knowledge of , or
knows completely. In this work, we present upper bounds (that
hold under both the average and maximal probability of error criteria) on the
capacity which hold for both deterministic and stochastic encoding schemes.Comment: To appear in the IEEE Transactions on Information Theory; shortened
version appeared at ISIT 201
Experimental Quantum Fingerprinting
Quantum communication holds the promise of creating disruptive technologies
that will play an essential role in future communication networks. For example,
the study of quantum communication complexity has shown that quantum
communication allows exponential reductions in the information that must be
transmitted to solve distributed computational tasks. Recently, protocols that
realize this advantage using optical implementations have been proposed. Here
we report a proof of concept experimental demonstration of a quantum
fingerprinting system that is capable of transmitting less information than the
best known classical protocol. Our implementation is based on a modified
version of a commercial quantum key distribution system using off-the-shelf
optical components over telecom wavelengths, and is practical for messages as
large as 100 Mbits, even in the presence of experimental imperfections. Our
results provide a first step in the development of experimental quantum
communication complexity.Comment: 11 pages, 6 Figure
The Capacity of Online (Causal) -ary Error-Erasure Channels
In the -ary online (or "causal") channel coding model, a sender wishes to
communicate a message to a receiver by transmitting a codeword symbol by symbol via a channel
limited to at most errors and/or erasures. The channel is
"online" in the sense that at the th step of communication the channel
decides whether to corrupt the th symbol or not based on its view so far,
i.e., its decision depends only on the transmitted symbols .
This is in contrast to the classical adversarial channel in which the
corruption is chosen by a channel that has a full knowledge on the sent
codeword .
In this work we study the capacity of -ary online channels for a combined
corruption model, in which the channel may impose at most {\em errors} and
at most {\em erasures} on the transmitted codeword. The online
channel (in both the error and erasure case) has seen a number of recent
studies which present both upper and lower bounds on its capacity. In this
work, we give a full characterization of the capacity as a function of ,
and .Comment: This is a new version of the binary case, which can be found at
arXiv:1412.637
Applications of Derandomization Theory in Coding
Randomized techniques play a fundamental role in theoretical computer science
and discrete mathematics, in particular for the design of efficient algorithms
and construction of combinatorial objects. The basic goal in derandomization
theory is to eliminate or reduce the need for randomness in such randomized
constructions. In this thesis, we explore some applications of the fundamental
notions in derandomization theory to problems outside the core of theoretical
computer science, and in particular, certain problems related to coding theory.
First, we consider the wiretap channel problem which involves a communication
system in which an intruder can eavesdrop a limited portion of the
transmissions, and construct efficient and information-theoretically optimal
communication protocols for this model. Then we consider the combinatorial
group testing problem. In this classical problem, one aims to determine a set
of defective items within a large population by asking a number of queries,
where each query reveals whether a defective item is present within a specified
group of items. We use randomness condensers to explicitly construct optimal,
or nearly optimal, group testing schemes for a setting where the query outcomes
can be highly unreliable, as well as the threshold model where a query returns
positive if the number of defectives pass a certain threshold. Finally, we
design ensembles of error-correcting codes that achieve the
information-theoretic capacity of a large class of communication channels, and
then use the obtained ensembles for construction of explicit capacity achieving
codes.
[This is a shortened version of the actual abstract in the thesis.]Comment: EPFL Phd Thesi
A characterization of the capacity of online (causal) binary channels
In the binary online (or "causal") channel coding model, a sender wishes to
communicate a message to a receiver by transmitting a codeword bit by bit via a channel limited to at most
corruptions. The channel is "online" in the sense that at the th step
of communication the channel decides whether to corrupt the th bit or not
based on its view so far, i.e., its decision depends only on the transmitted
bits . This is in contrast to the classical adversarial
channel in which the error is chosen by a channel that has a full knowledge on
the sent codeword .
In this work we study the capacity of binary online channels for two
corruption models: the {\em bit-flip} model in which the channel may flip at
most of the bits of the transmitted codeword, and the {\em erasure} model
in which the channel may erase at most bits of the transmitted codeword.
Specifically, for both error models we give a full characterization of the
capacity as a function of .
The online channel (in both the bit-flip and erasure case) has seen a number
of recent studies which present both upper and lower bounds on its capacity. In
this work, we present and analyze a coding scheme that improves on the
previously suggested lower bounds and matches the previously suggested upper
bounds thus implying a tight characterization
Quantum cryptography: key distribution and beyond
Uniquely among the sciences, quantum cryptography has driven both
foundational research as well as practical real-life applications. We review
the progress of quantum cryptography in the last decade, covering quantum key
distribution and other applications.Comment: It's a review on quantum cryptography and it is not restricted to QK
Describing quantum metrology with erasure errors using weight distributions of classical codes
Quantum sensors are expected to be a prominent use-case of quantum
technologies, but in practice, noise easily degrades their performance. Quantum
sensors can for instance be afflicted with erasure errors. Here, we consider
using quantum probe states with a structure that corresponds to classical
binary block codes of minimum distance . We obtain bounds
on the ultimate precision that these probe states can give for estimating the
unknown magnitude of a classical field after at most qubits of the quantum
probe state are erased. We show that the quantum Fisher information is
proportional to the variances of the weight distributions of the corresponding
shortened codes. If the shortened codes of a fixed code with
have a non-trivial weight distribution, then the probe states obtained by
concatenating this code with repetition codes of increasing length enable
asymptotically optimal field-sensing that passively tolerates up to erasure
errors