4,767 research outputs found
Reduced Dimensional Optimal Vector Linear Index Codes for Index Coding Problems with Symmetric Neighboring and Consecutive Side-information
A single unicast index coding problem (SUICP) with symmetric neighboring and
consecutive side-information (SNCS) has messages and receivers, the
th receiver wanting the th message and having the
side-information . The single unicast index coding problem with
symmetric neighboring and consecutive side-information, SUICP(SNCS), is
motivated by topological interference management problems in wireless
communication networks. Maleki, Cadambe and Jafar obtained the symmetric
capacity of this SUICP(SNCS) and proposed optimal length codes by using
Vandermonde matrices. In our earlier work, we gave optimal length
-dimensional vector linear index codes for SUICP(SNCS) satisfying some
conditions on and \cite{VaR1}. In this paper, for SUICP(SNCS) with
arbitrary and , we construct optimal length
-dimensional vector linear index codes. We
prove that the constructed vector linear index code is of minimal dimension if
is equal to . The proposed
construction gives optimal length scalar linear index codes for the SUICP(SNCS)
if divides both and . The proposed construction is independent
of field size and works over every field. We give a low-complexity decoding for
the SUICP(SNCS). By using the proposed decoding method, every receiver is able
to decode its wanted message symbol by simply adding some index code symbols
(broadcast symbols).Comment: 13 pages, 1 figure and 5 table
Elements of Cellular Blind Interference Alignment --- Aligned Frequency Reuse, Wireless Index Coding and Interference Diversity
We explore degrees of freedom (DoF) characterizations of partially connected
wireless networks, especially cellular networks, with no channel state
information at the transmitters. Specifically, we introduce three fundamental
elements --- aligned frequency reuse, wireless index coding and interference
diversity --- through a series of examples, focusing first on infinite regular
arrays, then on finite clusters with arbitrary connectivity and message sets,
and finally on heterogeneous settings with asymmetric multiple antenna
configurations. Aligned frequency reuse refers to the optimality of orthogonal
resource allocations in many cases, but according to unconventional reuse
patterns that are guided by interference alignment principles. Wireless index
coding highlights both the intimate connection between the index coding problem
and cellular blind interference alignment, as well as the added complexity
inherent to wireless settings. Interference diversity refers to the observation
that in a wireless network each receiver experiences a different set of
interferers, and depending on the actions of its own set of interferers, the
interference-free signal space at each receiver fluctuates differently from
other receivers, creating opportunities for robust applications of blind
interference alignment principles
Optimality of Orthogonal Access for One-dimensional Convex Cellular Networks
It is shown that a greedy orthogonal access scheme achieves the sum degrees
of freedom of all one-dimensional (all nodes placed along a straight line)
convex cellular networks (where cells are convex regions) when no channel
knowledge is available at the transmitters except the knowledge of the network
topology. In general, optimality of orthogonal access holds neither for
two-dimensional convex cellular networks nor for one-dimensional non-convex
cellular networks, thus revealing a fundamental limitation that exists only
when both one-dimensional and convex properties are simultaneously enforced, as
is common in canonical information theoretic models for studying cellular
networks. The result also establishes the capacity of the corresponding class
of index coding problems
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