52 research outputs found
Capacity of a POST Channel with and without Feedback
We consider finite state channels where the state of the channel is its
previous output. We refer to these as POST (Previous Output is the STate)
channels. We first focus on POST() channels. These channels have binary
inputs and outputs, where the state determines if the channel behaves as a
or an channel, both with parameter . %with parameter We
show that the non feedback capacity of the POST() channel equals its
feedback capacity, despite the memory of the channel. The proof of this
surprising result is based on showing that the induced output distribution,
when maximizing the directed information in the presence of feedback, can also
be achieved by an input distribution that does not utilize of the feedback. We
show that this is a sufficient condition for the feedback capacity to equal the
non feedback capacity for any finite state channel. We show that the result
carries over from the POST() channel to a binary POST channel where the
previous output determines whether the current channel will be binary with
parameters or . Finally, we show that, in general, feedback may
increase the capacity of a POST channel
Empowerment for Continuous Agent-Environment Systems
This paper develops generalizations of empowerment to continuous states.
Empowerment is a recently introduced information-theoretic quantity motivated
by hypotheses about the efficiency of the sensorimotor loop in biological
organisms, but also from considerations stemming from curiosity-driven
learning. Empowemerment measures, for agent-environment systems with stochastic
transitions, how much influence an agent has on its environment, but only that
influence that can be sensed by the agent sensors. It is an
information-theoretic generalization of joint controllability (influence on
environment) and observability (measurement by sensors) of the environment by
the agent, both controllability and observability being usually defined in
control theory as the dimensionality of the control/observation spaces. Earlier
work has shown that empowerment has various interesting and relevant
properties, e.g., it allows us to identify salient states using only the
dynamics, and it can act as intrinsic reward without requiring an external
reward. However, in this previous work empowerment was limited to the case of
small-scale and discrete domains and furthermore state transition probabilities
were assumed to be known. The goal of this paper is to extend empowerment to
the significantly more important and relevant case of continuous vector-valued
state spaces and initially unknown state transition probabilities. The
continuous state space is addressed by Monte-Carlo approximation; the unknown
transitions are addressed by model learning and prediction for which we apply
Gaussian processes regression with iterated forecasting. In a number of
well-known continuous control tasks we examine the dynamics induced by
empowerment and include an application to exploration and online model
learning
Anonymous Networking amidst Eavesdroppers
The problem of security against timing based traffic analysis in wireless
networks is considered in this work. An analytical measure of anonymity in
eavesdropped networks is proposed using the information theoretic concept of
equivocation. For a physical layer with orthogonal transmitter directed
signaling, scheduling and relaying techniques are designed to maximize
achievable network performance for any given level of anonymity. The network
performance is measured by the achievable relay rates from the sources to
destinations under latency and medium access constraints. In particular,
analytical results are presented for two scenarios:
For a two-hop network with maximum anonymity, achievable rate regions for a
general m x 1 relay are characterized when nodes generate independent Poisson
transmission schedules. The rate regions are presented for both strict and
average delay constraints on traffic flow through the relay.
For a multihop network with an arbitrary anonymity requirement, the problem
of maximizing the sum-rate of flows (network throughput) is considered. A
selective independent scheduling strategy is designed for this purpose, and
using the analytical results for the two-hop network, the achievable throughput
is characterized as a function of the anonymity level. The throughput-anonymity
relation for the proposed strategy is shown to be equivalent to an information
theoretic rate-distortion function
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