63,318 research outputs found
On AVCs with Quadratic Constraints
In this work we study an Arbitrarily Varying Channel (AVC) with quadratic
power constraints on the transmitter and a so-called "oblivious" jammer (along
with additional AWGN) under a maximum probability of error criterion, and no
private randomness between the transmitter and the receiver. This is in
contrast to similar AVC models under the average probability of error criterion
considered in [1], and models wherein common randomness is allowed [2] -- these
distinctions are important in some communication scenarios outlined below.
We consider the regime where the jammer's power constraint is smaller than
the transmitter's power constraint (in the other regime it is known no positive
rate is possible). For this regime we show the existence of stochastic codes
(with no common randomness between the transmitter and receiver) that enables
reliable communication at the same rate as when the jammer is replaced with
AWGN with the same power constraint. This matches known information-theoretic
outer bounds. In addition to being a stronger result than that in [1] (enabling
recovery of the results therein), our proof techniques are also somewhat more
direct, and hence may be of independent interest.Comment: A shorter version of this work will be send to ISIT13, Istanbul. 8
pages, 3 figure
Causality - Complexity - Consistency: Can Space-Time Be Based on Logic and Computation?
The difficulty of explaining non-local correlations in a fixed causal
structure sheds new light on the old debate on whether space and time are to be
seen as fundamental. Refraining from assuming space-time as given a priori has
a number of consequences. First, the usual definitions of randomness depend on
a causal structure and turn meaningless. So motivated, we propose an intrinsic,
physically motivated measure for the randomness of a string of bits: its length
minus its normalized work value, a quantity we closely relate to its Kolmogorov
complexity (the length of the shortest program making a universal Turing
machine output this string). We test this alternative concept of randomness for
the example of non-local correlations, and we end up with a reasoning that
leads to similar conclusions as in, but is conceptually more direct than, the
probabilistic view since only the outcomes of measurements that can actually
all be carried out together are put into relation to each other. In the same
context-free spirit, we connect the logical reversibility of an evolution to
the second law of thermodynamics and the arrow of time. Refining this, we end
up with a speculation on the emergence of a space-time structure on bit strings
in terms of data-compressibility relations. Finally, we show that logical
consistency, by which we replace the abandoned causality, it strictly weaker a
constraint than the latter in the multi-party case.Comment: 17 pages, 16 figures, small correction
Spatial Transportation Networks with Transfer Costs: Asymptotic Optimality of Hub and Spoke Models
Consider networks on vertices at average density 1 per unit area. We seek
a network that minimizes total length subject to some constraint on journey
times, averaged over source-destination pairs. Suppose journey times depend on
both route-length and number of hops. Then for the constraint corresponding to
an average of 3 hops, the length of the optimal network scales as .
Alternatively, constraining the average number of hops to be 2 forces the
network length to grow slightly faster than order . Finally, if we
require the network length to be O(n) then the mean number of hops grows as
order . Each result is an upper bound in the worst case (of vertex
positions), and a lower bound under randomness or equidistribution assumptions.
The upper bounds arise in simple hub and spoke models, which are therefore
optimal in an order of magnitude sense
Variable-Length Intrinsic Randomness Allowing Positive Value of the Average Variational Distance
This paper considers the problem of variable-length intrinsic randomness. We
propose the average variational distance as the performance criterion from the
viewpoint of a dual relationship with the problem formulation of
variable-length resolvability. Previous study has derived the general formula
of the -variable-length resolvability. We derive the general formula
of the -variable-length intrinsic randomness. Namely, we characterize
the supremum of the mean length under the constraint that the value of the
average variational distance is smaller than or equal to a constant .
Our result clarifies a dual relationship between the general formula of
-variable-length resolvability and that of -variable-length
intrinsic randomness. We also derive a lower bound of the quantity
characterizing our general formula
Secret message capacity of a line network
We investigate the problem of information theoretically secure communication
in a line network with erasure channels and state feedback. We consider a
spectrum of cases for the private randomness that intermediate nodes can
generate, ranging from having intermediate nodes generate unlimited private
randomness, to having intermediate nodes generate no private randomness, and
all cases in between. We characterize the secret message capacity when either
only one of the channels is eavesdropped or all of the channels are
eavesdropped, and we develop polynomial time algorithms that achieve these
capacities. We also give an outer bound for the case where an arbitrary number
of channels is eavesdropped. Our work is the first to characterize the secrecy
capacity of a network of arbitrary size, with imperfect channels and feedback.
As a side result, we derive the secret key and secret message capacity of an
one-hop network, when the source has limited randomness
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