4,148 research outputs found
Generalized Interlinked Cycle Cover for Index Coding
A source coding problem over a noiseless broadcast channel where the source
is pre-informed about the contents of the cache of all receivers, is an index
coding problem. Furthermore, if each message is requested by one receiver, then
we call this an index coding problem with a unicast message setting. This
problem can be represented by a directed graph. In this paper, we first define
a structure (we call generalized interlinked cycles (GIC)) in directed graphs.
A GIC consists of cycles which are interlinked in some manner (i.e., not
disjoint), and it turns out that the GIC is a generalization of cliques and
cycles. We then propose a simple scalar linear encoding scheme with linear time
encoding complexity. This scheme exploits GICs in the digraph. We prove that
our scheme is optimal for a class of digraphs with message packets of any
length. Moreover, we show that our scheme can outperform existing techniques,
e.g., partial clique cover, local chromatic number, composite-coding, and
interlinked cycle cover.Comment: Extended version of the paper which is to be presented at the IEEE
Information Theory Workshop (ITW), 2015 Jej
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
Lost in translation: Toward a formal model of multilevel, multiscale medicine
For a broad spectrum of low level cognitive regulatory and other biological phenomena, isolation from signal crosstalk between them requires more metabolic free energy than permitting correlation. This allows an evolutionary exaptation leading to dynamic global broadcasts of interacting physiological processes at multiple scales. The argument is similar to the well-studied exaptation of noise to trigger stochastic resonance amplification in physiological subsystems. Not only is the living state characterized by cognition at every scale and level of organization, but by multiple, shifting, tunable, cooperative larger scale broadcasts that link selected subsets of functional modules to address problems. This multilevel dynamical viewpoint has implications for initiatives in translational medicine that have followed the implosive collapse of pharmaceutical industry 'magic bullet' research. In short, failure to respond to the inherently multilevel, multiscale nature of human pathophysiology will doom translational medicine to a similar implosion
Graph-Theoretic Approaches to Two-Sender Index Coding
Consider a communication scenario over a noiseless channel where a sender is
required to broadcast messages to multiple receivers, each having side
information about some messages. In this scenario, the sender can leverage the
receivers' side information during the encoding of messages in order to reduce
the required transmissions. This type of encoding is called index coding. In
this paper, we study index coding with two cooperative senders, each with some
subset of messages, and multiple receivers, each requesting one unique message.
The index coding in this setup is called two-sender unicast index coding
(TSUIC). The main aim of TSUIC is to minimize the total number of transmissions
required by the two senders. Based on graph-theoretic approaches, we prove that
TSUIC is equivalent to single-sender unicast index coding (SSUIC) for some
special cases. Moreover, we extend the existing schemes for SSUIC, viz., the
cycle-cover scheme, the clique-cover scheme, and the local-chromatic scheme to
the corresponding schemes for TSUIC.Comment: To be presented at 2016 IEEE Global Communications Conference
(GLOBECOM 2016) Workshop on Network Coding and Applications (NetCod),
Washington, USA, 201
Crosstalk and the spectrum of biological global broadcasts: Toward generalization of the Baars consciousness model across physiological subsystems
Once cognitive biological phenomena are recognized as necessarily having 'dual' information sources, it is easy to show that the information theory chain rule implies isolating coresident information sources from crosstalk requires more metabolic free energy than permitting correlation. This provides conditions for an evolutionary exaptation leading to dynamic global broadcasts of interacting cognitive biological processes analogous to, but slower than, consciousness, itself included within the paradigm. The argument is closely analogous to the well-studied exaptation of noise to trigger stochastic resonance amplification in physiological systems
The Single-Uniprior Index-Coding Problem: The Single-Sender Case and The Multi-Sender Extension
Index coding studies multiterminal source-coding problems where a set of
receivers are required to decode multiple (possibly different) messages from a
common broadcast, and they each know some messages a priori. In this paper, at
the receiver end, we consider a special setting where each receiver knows only
one message a priori, and each message is known to only one receiver. At the
broadcasting end, we consider a generalized setting where there could be
multiple senders, and each sender knows a subset of the messages. The senders
collaborate to transmit an index code. This work looks at minimizing the number
of total coded bits the senders are required to transmit. When there is only
one sender, we propose a pruning algorithm to find a lower bound on the optimal
(i.e., the shortest) index codelength, and show that it is achievable by linear
index codes. When there are two or more senders, we propose an appending
technique to be used in conjunction with the pruning technique to give a lower
bound on the optimal index codelength; we also derive an upper bound based on
cyclic codes. While the two bounds do not match in general, for the special
case where no two distinct senders know any message in common, the bounds
match, giving the optimal index codelength. The results are expressed in terms
of strongly connected components in directed graphs that represent the
index-coding problems.Comment: Author final manuscrip
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