12,157 research outputs found
Capacity of 1-to-K Broadcast Packet Erasure Channels with Channel Output Feedback
This paper focuses on the 1-to-K broadcast packet erasure channel (PEC),
which is a generalization of the broadcast binary erasure channel from the
binary symbol to that of arbitrary finite fields GF(q) with sufficiently large
q. We consider the setting in which the source node has instant feedback of the
channel outputs of the K receivers after each transmission. Such a setting
directly models network coded packet transmission in the downlink direction
with integrated feedback mechanisms (such as Automatic Repeat reQuest (ARQ)).
The main results of this paper are: (i) The capacity region for general
1-to-3 broadcast PECs, and (ii) The capacity region for two classes of 1-to-K
broadcast PECs: the symmetric PECs, and the spatially independent PECs with
one-sided fairness constraints. This paper also develops (iii) A pair of outer
and inner bounds of the capacity region for arbitrary 1-to-K broadcast PECs,
which can be evaluated by any linear programming solver. For most practical
scenarios, the outer and inner bounds meet and thus jointly characterize the
capacity.Comment: 8 pages, 2 figures. Published in Allerton 2010. The journal version
of this work was submitted to IEEE Trans IT in May, 201
Charged Fluid Dynamics in Scalar-Tensor Theories of Gravity with Torsion
n scalar-tensor theories of gravity with torsion, the gravitational field is
described in terms of a symmetric metric tensor , a metric-compatible
connection with torsion, and a scalar field . The main aim is to
explore an interaction of a charged perfect fluid and a scalar field in
a background electromagnetic and gravitational field described by \{,
, \}. The interaction is based on an action functional of a
charged perfect fluid that is invariant under global conformal rescalings.
Using a variational principle, we obtain equations of motion for the charged
perfect fluid. Moreover, we verify that these equations of motion are
equivalent to the gauge identities obtained from the invariance of an action
functional under spacetime dffeomorphisms and a local U(1) gauge group.Comment: 4 page
When and By How Much Can Helper Node Selection Improve Regenerating Codes?
Regenerating codes (RCs) can significantly reduce the repair-bandwidth of
distributed storage networks. Initially, the analysis of RCs was based on the
assumption that during the repair process, the newcomer does not distinguish
(among all surviving nodes) which nodes to access, i.e., the newcomer is
oblivious to the set of helpers being used. Such a scheme is termed the blind
repair (BR) scheme. Nonetheless, it is intuitive in practice that the newcomer
should choose to access only those "good" helpers. In this paper, a new
characterization of the effect of choosing the helper nodes in terms of the
storage-bandwidth tradeoff is given. Specifically, answers to the following
fundamental questions are given: Under what conditions does proactively
choosing the helper nodes improve the storage-bandwidth tradeoff? Can this
improvement be analytically quantified?
This paper answers the former question by providing a necessary and
sufficient condition under which optimally choosing good helpers strictly
improves the storage-bandwidth tradeoff. To answer the latter question, a
low-complexity helper selection solution, termed the family repair (FR) scheme,
is proposed and the corresponding storage/repair-bandwidth curve is
characterized. For example, consider a distributed storage network with 60
total number of nodes and the network is resilient against 50 node failures. If
the number of helper nodes is 10, then the FR scheme and its variant
demonstrate 27% reduction in the repair-bandwidth when compared to the BR
solution. This paper also proves that under some design parameters, the FR
scheme is indeed optimal among all helper selection schemes. An explicit
construction of an exact-repair code is also proposed that can achieve the
minimum-bandwidth-regenerating point of the FR scheme. The new exact-repair
code can be viewed as a generalization of the existing fractional repetition
code.Comment: 35 pages, 10 figures, submitted to IEEE Transactions on Information
Theory on September 04, 201
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