196,796 research outputs found
A class of index coding problems with rate 1/3
An index coding problem with messages has symmetric rate if all
messages can be conveyed at rate . In a recent work, a class of index coding
problems for which symmetric rate is achievable was characterised
using special properties of the side-information available at the receivers. In
this paper, we show a larger class of index coding problems (which includes the
previous class of problems) for which symmetric rate is
achievable. In the process, we also obtain a stricter necessary condition for
rate feasibility than what is known in literature.Comment: Shorter version submitted to ISIT 201
Optimal Index Codes via a Duality between Index Coding and Network Coding
In Index Coding, the goal is to use a broadcast channel as efficiently as
possible to communicate information from a source to multiple receivers which
can possess some of the information symbols at the source as side-information.
In this work, we present a duality relationship between index coding (IC) and
multiple-unicast network coding (NC). It is known that the IC problem can be
represented using a side-information graph (with number of vertices
equal to the number of source symbols). The size of the maximum acyclic induced
subgraph, denoted by is a lower bound on the \textit{broadcast rate}.
For IC problems with and , prior work has shown that
binary (over ) linear index codes achieve the lower bound
for the broadcast rate and thus are optimal. In this work, we use the the
duality relationship between NC and IC to show that for a class of IC problems
with , binary linear index codes achieve the lower bound on
the broadcast rate. In contrast, it is known that there exists IC problems with
and optimal broadcast rate strictly greater than
On Critical Index Coding Problems
The question of under what condition some side information for index coding
can be removed without affecting the capacity region is studied, which was
originally posed by Tahmasbi, Shahrasbi, and Gohari. To answer this question,
the notion of unicycle for the side information graph is introduced and it is
shown that any edge that belongs to a unicycle is critical, namely, it cannot
be removed without reducing the capacity region. Although this sufficient
condition for criticality is not necessary in general, a partial converse is
established, which elucidates the connection between the notion of unicycle and
the maximal acylic induced subgraph outer bound on the capacity region by
Bar-Yossef, Birk, Jayram, and Kol.Comment: 5 pages, accepted to 2015 IEEE Information Theory Workshop (ITW),
Jeju Island, Kore
Index Coding: Rank-Invariant Extensions
An index coding (IC) problem consisting of a server and multiple receivers
with different side-information and demand sets can be equivalently represented
using a fitting matrix. A scalar linear index code to a given IC problem is a
matrix representing the transmitted linear combinations of the message symbols.
The length of an index code is then the number of transmissions (or
equivalently, the number of rows in the index code). An IC problem is called an extension of another IC problem if the
fitting matrix of is a submatrix of the fitting matrix of . We first present a straightforward \textit{-order} extension
of an IC problem for which an index code is
obtained by concatenating copies of an index code of . The length
of the codes is the same for both and , and if the
index code for has optimal length then so does the extended code for
. More generally, an extended IC problem of having
the same optimal length as is said to be a \textit{rank-invariant}
extension of . We then focus on -order rank-invariant extensions
of , and present constructions of such extensions based on involutory
permutation matrices
PointMap: A real-time memory-based learning system with on-line and post-training pruning
Also published in the International Journal of Hybrid Intelligent Systems, Volume 1, January, 2004A memory-based learning system called PointMap is a simple and computationally efficient extension of Condensed Nearest Neighbor that allows the user to limit the number of exemplars stored during incremental learning. PointMap evaluates the information value of coding nodes during training, and uses this index to prune uninformative nodes either on-line or after training. These pruning methods allow the user to control both a priori code size and sensitivity to detail in the training data, as well as to determine the code size necessary for accurate performance on a given data set. Coding and pruning computations are local in space, with only the nearest coded neighbor available for comparison with the input; and in time, with only the current input available during coding. Pruning helps solve common problems of traditional memory-based learning systems: large memory requirements, their accompanying slow on-line computations, and sensitivity to noise. PointMap copes with the curse of dimensionality by considering multiple nearest neighbors during testing without increasing the complexity of the training process or the stored code. The performance of PointMap is compared to that of a group of sixteen nearest-neighbor systems on benchmark problems.This research was supported by grants from the Air Force Office of Scientific Research (AFOSR F49620-98-l-0108, F49620-0l-l-0397, and F49620-0l-l-0423)
and the Office of Naval Research (ONR N00014-0l-l-0624)
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