38 research outputs found
On the Capacity Region for Index Coding
A new inner bound on the capacity region of a general index coding problem is
established. Unlike most existing bounds that are based on graph theoretic or
algebraic tools, the bound is built on a random coding scheme and optimal
decoding, and has a simple polymatroidal single-letter expression. The utility
of the inner bound is demonstrated by examples that include the capacity region
for all index coding problems with up to five messages (there are 9846
nonisomorphic ones).Comment: 5 pages, 6 figures, accepted to the 2013 IEEE International Symposium
on Information Theory (ISIT), Istanbul, Turkey, July 201
On a Duality Between Recoverable Distributed Storage and Index Coding
In this paper, we introduce a model of a single-failure locally recoverable
distributed storage system. This model appears to give rise to a problem
seemingly dual of the well-studied index coding problem. The relation between
the dimensions of an optimal index code and optimal distributed storage code of
our model has been established in this paper. We also show some extensions to
vector codes.Comment: A small new section and new references added. A minor error corrected
from the previous versio
On the Capacity Region for Secure Index Coding
We study the index coding problem in the presence of an eavesdropper, where
the aim is to communicate without allowing the eavesdropper to learn any single
message aside from the messages it may already know as side information. We
establish an outer bound on the underlying secure capacity region of the index
coding problem, which includes polymatroidal and security constraints, as well
as the set of additional decoding constraints for legitimate receivers. We then
propose a secure variant of the composite coding scheme, which yields an inner
bound on the secure capacity region of the index coding problem. For the
achievability of secure composite coding, a secret key with vanishingly small
rate may be needed to ensure that each legitimate receiver who wants the same
message as the eavesdropper, knows at least two more messages than the
eavesdropper. For all securely feasible index coding problems with four or
fewer messages, our numerical results establish the secure index coding
capacity region
Coded Cooperative Data Exchange for a Secret Key
We consider a coded cooperative data exchange problem with the goal of
generating a secret key. Specifically, we investigate the number of public
transmissions required for a set of clients to agree on a secret key with
probability one, subject to the constraint that it remains private from an
eavesdropper.
Although the problems are closely related, we prove that secret key
generation with fewest number of linear transmissions is NP-hard, while it is
known that the analogous problem in traditional cooperative data exchange can
be solved in polynomial time. In doing this, we completely characterize the
best possible performance of linear coding schemes, and also prove that linear
codes can be strictly suboptimal. Finally, we extend the single-key results to
characterize the minimum number of public transmissions required to generate a
desired integer number of statistically independent secret keys.Comment: Full version of a paper that appeared at ISIT 2014. 19 pages, 2
figure
TDMA is Optimal for All-unicast DoF Region of TIM if and only if Topology is Chordal Bipartite
The main result of this work is that an orthogonal access scheme such as TDMA
achieves the all-unicast degrees of freedom (DoF) region of the topological
interference management (TIM) problem if and only if the network topology graph
is chordal bipartite, i.e., every cycle that can contain a chord, does contain
a chord. The all-unicast DoF region includes the DoF region for any arbitrary
choice of a unicast message set, so e.g., the results of Maleki and Jafar on
the optimality of orthogonal access for the sum-DoF of one-dimensional convex
networks are recovered as a special case. The result is also established for
the corresponding topological representation of the index coding problem
Fundamental Limits of Caching
Caching is a technique to reduce peak traffic rates by prefetching popular
content into memories at the end users. Conventionally, these memories are used
to deliver requested content in part from a locally cached copy rather than
through the network. The gain offered by this approach, which we term local
caching gain, depends on the local cache size (i.e, the memory available at
each individual user). In this paper, we introduce and exploit a second,
global, caching gain not utilized by conventional caching schemes. This gain
depends on the aggregate global cache size (i.e., the cumulative memory
available at all users), even though there is no cooperation among the users.
To evaluate and isolate these two gains, we introduce an
information-theoretic formulation of the caching problem focusing on its basic
structure. For this setting, we propose a novel coded caching scheme that
exploits both local and global caching gains, leading to a multiplicative
improvement in the peak rate compared to previously known schemes. In
particular, the improvement can be on the order of the number of users in the
network. Moreover, we argue that the performance of the proposed scheme is
within a constant factor of the information-theoretic optimum for all values of
the problem parameters.Comment: To appear in IEEE Transactions on Information Theor