37 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
Recommended from our members
Fundamental Limits of Network Communication with General Message Sets: A Combinatorial Approach
The classical theoretical framework for communication networks is based on the simplifying assumption that each message to be sent is known to a single transmitter and intended for a single receiver. Modern communication protocols reflect this framework by treating the physical layer as a network of individual links. However, this wireline view of wireless communications fails to account for the heterogeneous nature of network demands, consisting of both unicast and multicast services, and can fail to leverage the inherent broadcast advantage of the wireless medium.
This thesis extends the classical framework of a private-message interface to the physical layer to one with both private and common messages. A key difficulty, in both the description and analysis of a communication model with general messages sets, is that there are combinatorially many message possibilities. With order-theoretic language and tools from combinatorial optimization and graphical models, we develop a general framework for characterizing the fundamental limits of information transfer over large many-to-one (multiple access) and one-to-many (broadcast) communication channels with general message sets. In particular, achievable regions are proposed for arbitrary such channels. For the multiple-access channel, the achievable region is optimal, and the order-theoretic perspective both unifies and extends previous results. For the broadcast channel, the region is specialized to an inner bound to the Degree of Freedom region, a setting where it is provably optimal in select cases.
This thesis provides fresh insights into the long-standing random coding technique of superposition coding to arrive at these results. Governing constraints on reliable communication through superposition coding are shown to be polymatroidal over a lattice of subsets that may not be the boolean lattice of all subsets. Permissible input distributions for superposition coding are concisely characterized through directed graphical models of conditional dependencies. The two-user interference channel is also addressed, where the state-of-the art is extended from the case with two private messages to one with an additional common message
Network Information Flow with Correlated Sources
In this paper, we consider a network communications problem in which multiple
correlated sources must be delivered to a single data collector node, over a
network of noisy independent point-to-point channels. We prove that perfect
reconstruction of all the sources at the sink is possible if and only if, for
all partitions of the network nodes into two subsets S and S^c such that the
sink is always in S^c, we have that H(U_S|U_{S^c}) < \sum_{i\in S,j\in S^c}
C_{ij}. Our main finding is that in this setup a general source/channel
separation theorem holds, and that Shannon information behaves as a classical
network flow, identical in nature to the flow of water in pipes. At first
glance, it might seem surprising that separation holds in a fairly general
network situation like the one we study. A closer look, however, reveals that
the reason for this is that our model allows only for independent
point-to-point channels between pairs of nodes, and not multiple-access and/or
broadcast channels, for which separation is well known not to hold. This
``information as flow'' view provides an algorithmic interpretation for our
results, among which perhaps the most important one is the optimality of
implementing codes using a layered protocol stack.Comment: Final version, to appear in the IEEE Transactions on Information
Theory -- contains (very) minor changes based on the last round of review