966 research outputs found
A Practical Approach for Successive Omniscience
The system that we study in this paper contains a set of users that observe a
discrete memoryless multiple source and communicate via noise-free channels
with the aim of attaining omniscience, the state that all users recover the
entire multiple source. We adopt the concept of successive omniscience (SO),
i.e., letting the local omniscience in some user subset be attained before the
global omniscience in the entire system, and consider the problem of how to
efficiently attain omniscience in a successive manner. Based on the existing
results on SO, we propose a CompSetSO algorithm for determining a complimentary
set, a user subset in which the local omniscience can be attained first without
increasing the sum-rate, the total number of communications, for the global
omniscience. We also derive a sufficient condition for a user subset to be
complimentary so that running the CompSetSO algorithm only requires a lower
bound, instead of the exact value, of the minimum sum-rate for attaining global
omniscience. The CompSetSO algorithm returns a complimentary user subset in
polynomial time. We show by example how to recursively apply the CompSetSO
algorithm so that the global omniscience can be attained by multi-stages of SO
On the Communication Complexity of Secret Key Generation in the Multiterminal Source Model
Communication complexity refers to the minimum rate of public communication
required for generating a maximal-rate secret key (SK) in the multiterminal
source model of Csiszar and Narayan. Tyagi recently characterized this
communication complexity for a two-terminal system. We extend the ideas in
Tyagi's work to derive a lower bound on communication complexity in the general
multiterminal setting. In the important special case of the complete graph
pairwise independent network (PIN) model, our bound allows us to determine the
exact linear communication complexity, i.e., the communication complexity when
the communication and SK are restricted to be linear functions of the
randomness available at the terminals.Comment: A 5-page version of this manuscript will be submitted to the 2014
IEEE International Symposium on Information Theory (ISIT 2014
On the Public Communication Needed to Achieve SK Capacity in the Multiterminal Source Model
The focus of this paper is on the public communication required for
generating a maximal-rate secret key (SK) within the multiterminal source model
of Csisz{\'a}r and Narayan. Building on the prior work of Tyagi for the
two-terminal scenario, we derive a lower bound on the communication complexity,
, defined to be the minimum rate of public communication needed
to generate a maximal-rate SK. It is well known that the minimum rate of
communication for omniscience, denoted by , is an upper bound on
. For the class of pairwise independent network (PIN) models
defined on uniform hypergraphs, we show that a certain "Type "
condition, which is verifiable in polynomial time, guarantees that our lower
bound on meets the upper bound. Thus, PIN
models satisfying our condition are -maximal, meaning that the
upper bound holds with equality. This allows
us to explicitly evaluate for such PIN models. We also give
several examples of PIN models that satisfy our Type condition.
Finally, we prove that for an arbitrary multiterminal source model, a stricter
version of our Type condition implies that communication from
\emph{all} terminals ("omnivocality") is needed for establishing a SK of
maximum rate. For three-terminal source models, the converse is also true:
omnivocality is needed for generating a maximal-rate SK only if the strict Type
condition is satisfied. Counterexamples exist that show that the
converse is not true in general for source models with four or more terminals.Comment: Submitted to the IEEE Transactions on Information Theory. arXiv admin
note: text overlap with arXiv:1504.0062
Cooperative Data Exchange based on MDS Codes
The cooperative data exchange problem is studied for the fully connected
network. In this problem, each node initially only possesses a subset of the
packets making up the file. Nodes make broadcast transmissions that are
received by all other nodes. The goal is for each node to recover the full
file. In this paper, we present a polynomial-time deterministic algorithm to
compute the optimal (i.e., minimal) number of required broadcast transmissions
and to determine the precise transmissions to be made by the nodes. A
particular feature of our approach is that {\it each} of the
transmissions is a linear combination of {\it exactly} packets, and we
show how to optimally choose the value of We also show how the
coefficients of these linear combinations can be chosen by leveraging a
connection to Maximum Distance Separable (MDS) codes. Moreover, we show that
our method can be used to solve cooperative data exchange problems with
weighted cost as well as the so-called successive local omniscience problem.Comment: 21 pages, 1 figur
New Protocols for Conference Key and Multipartite Entanglement Distillation
We approach two interconnected problems of quantum information processing in
networks: Conference key agreement and entanglement distillation, both in the
so-called source model where the given resource is a multipartite quantum state
and the players interact over public classical channels to generate the desired
correlation. The first problem is the distillation of a conference key when the
source state is shared between a number of legal players and an eavesdropper;
the eavesdropper, apart from starting off with this quantum side information,
also observes the public communication between the players. The second is the
distillation of Greenberger-Horne-Zeilinger (GHZ) states by means of local
operations and classical communication (LOCC) from the given mixed state. These
problem settings extend our previous paper [IEEE Trans. Inf. Theory
68(2):976-988, 2022], and we generalise its results: using a quantum version of
the task of communication for omniscience, we derive novel lower bounds on the
distillable conference key from any multipartite quantum state by means of
non-interacting communication protocols. Secondly, we establish novel lower
bounds on the yield of GHZ states from multipartite mixed states. Namely, we
present two methods to produce bipartite entanglement between sufficiently many
nodes so as to produce GHZ states. Next, we show that the conference key
agreement protocol can be made coherent under certain conditions, enabling the
direct generation of multipartite GHZ states
INFORMATION THEORETIC SECRET KEY GENERATION: STRUCTURED CODES AND TREE PACKING
This dissertation deals with a multiterminal source model for
secret key generation by multiple network terminals with prior and
privileged access to a set of correlated signals complemented by
public discussion among themselves. Emphasis is placed on a
characterization of secret key capacity, i.e., the largest rate of
an achievable secret key, and on algorithms for key construction.
Various information theoretic security requirements of increasing
stringency: weak, strong and perfect secrecy, as well as different
types of sources: finite-valued and continuous, are studied.
Specifically, three different models are investigated.
First, we consider strong secrecy generation for a
discrete multiterminal source model. We discover a
connection between secret key capacity and a new
source coding concept of ``minimum information rate for signal dissemination,''
that is of independent interest in multiterminal data compression.
Our main contribution is to show for this discrete model
that structured linear codes suffice to generate a
strong secret key of the best rate.
Second, strong secrecy generation is considered for models with
continuous observations, in particular jointly Gaussian signals.
In the absence of suitable analogs of source coding notions for
the previous discrete model, new techniques are required for a
characterization of secret key capacity as well as for the design
of algorithms for secret key generation. Our proof of the secret
key capacity result, in particular the converse proof, as well as
our capacity-achieving algorithms for secret key construction
based on structured codes and quantization for a model with two
terminals, constitute the two main contributions for this second
model.
Last, we turn our attention to perfect secrecy generation for
fixed signal observation lengths as well as for their asymptotic
limits. In contrast with the analysis of the previous two models
that relies on probabilistic techniques, perfect secret key
generation bears the essence of ``zero-error information theory,''
and accordingly, we rely on mathematical techniques of a
combinatorial nature. The model under consideration is the
``Pairwise Independent Network'' (PIN) model in which every pair
of terminals share a random binary string, with the strings shared
by distinct pairs of terminals being mutually independent. This
model, which is motivated by practical aspects of a wireless
communication network in which terminals communicate on the same
frequency, results in three main contributions. First, the
concept of perfect omniscience in data compression leads to a
single-letter formula for the perfect secret key capacity of the
PIN model; moreover, this capacity is shown to be achieved by
linear noninteractive public communication, and coincides with
strong secret key capacity. Second, taking advantage of a
multigraph representation of the PIN model, we put forth an
efficient algorithm for perfect secret key generation based on a
combinatorial concept of maximal packing of Steiner trees of the
multigraph. When all the terminals seek to share perfect secrecy,
the algorithm is shown to achieve capacity. When only a subset of
terminals wish to share perfect secrecy, the algorithm is shown to
achieve at least half of it. Additionally, we obtain nonasymptotic
and asymptotic bounds on the size and rate of the best perfect
secret key generated by the algorithm. These bounds are of
independent interest from a purely graph theoretic viewpoint as
they constitute new estimates for the maximum size and rate of
Steiner tree packing of a given multigraph. Third, a particular
configuration of the PIN model arises when a lone ``helper''
terminal aids all the other ``user'' terminals generate perfect
secrecy. This model has special features that enable us to obtain
necessary and sufficient conditions for Steiner tree packing to
achieve perfect secret key capacity
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